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Volumn 13, Issue , 2004, Pages 55-145

The numerical analysis of functional integral and integro-differential equations of Volterra type

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EID: 2942644332     PISSN: 09624929     EISSN: None     Source Type: Journal    
DOI: 10.1017/cbo9780511569975.002     Document Type: Review
Times cited : (33)

References (273)
  • 2
    • 0007145654 scopus 로고
    • Sulle equazioni integrali
    • G. Andreoli (1914), 'Sulle equazioni integrali', Rend. Circ. Mat. Palermo 37, 76-112.
    • (1914) Rend. Circ. Mat. Palermo , vol.37 , pp. 76-112
    • Andreoli, G.1
  • 4
    • 0001690579 scopus 로고
    • The numerical solution of delay-differential-algebraic equations of retarded and neutral type
    • U. Ascher and L. R. Petzold (1995), 'The numerical solution of delay-differential-algebraic equations of retarded and neutral type', SIAM J. Numer. Anal. 32, 1635-1657.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1635-1657
    • Ascher, U.1    Petzold, L.R.2
  • 5
    • 0042724819 scopus 로고
    • Continuous Volterra-Runge-Kutta methods for integral equations with pure delay
    • N. Baddour and H. Brunner (1993), 'Continuous Volterra-Runge-Kutta methods for integral equations with pure delay'. Computing 50, 213-227.
    • (1993) Computing , vol.50 , pp. 213-227
    • Baddour, N.1    Brunner, H.2
  • 6
    • 0039721560 scopus 로고    scopus 로고
    • Numerical analysis of Volterra functional and integral equations
    • I. S. Duff and G. A. Watson, eds, Clarendon Press. Oxford
    • C. T. H. Baker (1997), 'Numerical analysis of Volterra functional and integral equations', in The State of the Art in Numerical Analysis (I. S. Duff and G. A. Watson, eds), Clarendon Press. Oxford, pp. 193-222.
    • (1997) The State of the Art in Numerical Analysis , pp. 193-222
    • Baker, C.T.H.1
  • 7
    • 0034517076 scopus 로고    scopus 로고
    • A perspective on the numerical treatment of Volterra equations
    • C. T. H. Baker (2000), 'A perspective on the numerical treatment of Volterra equations'. J. Comput. Appl. Math. 125, 217-249.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 217-249
    • Baker, C.T.H.1
  • 8
    • 38249019058 scopus 로고
    • R-K formulae applied to Volterra equations with delay
    • C. T. H. Baker and M. S. Derakhshan (1990), 'R-K formulae applied to Volterra equations with delay', J. Comput. Appl. Math. 29, 293-310.
    • (1990) J. Comput. Appl. Math. , vol.29 , pp. 293-310
    • Baker, C.T.H.1    Derakhshan, M.S.2
  • 9
    • 0030635428 scopus 로고    scopus 로고
    • Pitfalls in parameter estimation for delay differential equations
    • C. T. H. Baker and C. A. H. Paul (1997), 'Pitfalls in parameter estimation for delay differential equations', SIAM J. Sci. Comput. 18, 305-314.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 305-314
    • Baker, C.T.H.1    Paul, C.A.H.2
  • 10
    • 0001442051 scopus 로고
    • Issues in the numerical solution of evolutionary delay differential equations
    • C. T. H. Baker, C. A. H. Paul and D. R. Willé (1995), 'Issues in the numerical solution of evolutionary delay differential equations', Adv. Comput. Math. 3, 171-196.
    • (1995) Adv. Comput. Math. , vol.3 , pp. 171-196
    • Baker, C.T.H.1    Paul, C.A.H.2    Willé, D.R.3
  • 11
    • 0031207491 scopus 로고    scopus 로고
    • Stability analysis of continuous implicit Runge-Kutta methods for Volterra integro-differential systems with unbounded delays
    • C. T. H. Baker and A. Tang (1997), 'Stability analysis of continuous implicit Runge-Kutta methods for Volterra integro-differential systems with unbounded delays'. Appl. Numer. Math. 24, 153-173.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 153-173
    • Baker, C.T.H.1    Tang, A.2
  • 13
    • 0001331423 scopus 로고
    • Spline approximations to functional differential equations
    • H. T. Banks and F. Kappel (1979), 'Spline approximations to functional differential equations'. J. Differential Equations 34, 496-522.
    • (1979) J. Differential Equations , vol.34 , pp. 496-522
    • Banks, H.T.1    Kappel, F.2
  • 14
    • 25044478087 scopus 로고
    • Sur une équation différentielle fonctionnelle analytique
    • J. Bélair (1981), 'Sur une équation différentielle fonctionnelle analytique', Canad. Math. Bull. 24, 43-46.
    • (1981) Canad. Math. Bull. , vol.24 , pp. 43-46
    • Bélair, J.1
  • 15
    • 0000194431 scopus 로고
    • Population models with state-dependent delays
    • O. Arino, D. E. Axelrod and M. Kimmel, eds, Marcel Dekker, New York
    • J. Bélair (1991), 'Population models with state-dependent delays', in Mathematical Population Dynamics (O. Arino, D. E. Axelrod and M. Kimmel, eds), Marcel Dekker, New York, pp. 165-176.
    • (1991) Mathematical Population Dynamics , pp. 165-176
    • Bélair, J.1
  • 16
    • 0021449148 scopus 로고
    • One-step collocation for delay differential equations
    • A. Bellen (1984), 'One-step collocation for delay differential equations', J. Comput. Appl. Math. 10, 275-283.
    • (1984) J. Comput. Appl. Math. , vol.10 , pp. 275-283
    • Bellen, A.1
  • 17
    • 0005626254 scopus 로고
    • Constrained mesh methods for functional-differential equations
    • Delay Equations, Approximation and Application (G. Meinardus and G. Nürnberger, eds), Birkhäuser, Basel/Boston
    • A. Bellen (1985), 'Constrained mesh methods for functional-differential equations', in Delay Equations, Approximation and Application (G. Meinardus and G. Nürnberger, eds), Vol. 74 of International Series of Numerical Mathematics, Birkhäuser, Basel/Boston, pp. 52-70.
    • (1985) International Series of Numerical Mathematics , vol.74 , pp. 52-70
    • Bellen, A.1
  • 18
    • 0031208947 scopus 로고    scopus 로고
    • Contractivity of continuous Runge-Kutta methods for delay differential equations
    • A. Bellen (1997), 'Contractivity of continuous Runge-Kutta methods for delay differential equations', Appl. Numer. Math. 24, 219-232.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 219-232
    • Bellen, A.1
  • 19
    • 0036031976 scopus 로고    scopus 로고
    • Preservation of superconvergence in the numerical integration of delay differential equations with proportional delay
    • A. Bellen (2001), 'Preservation of superconvergence in the numerical integration of delay differential equations with proportional delay', IMA J. Numer. Anal. 22, 529-536.
    • (2001) IMA J. Numer. Anal. , vol.22 , pp. 529-536
    • Bellen, A.1
  • 21
    • 0031211264 scopus 로고    scopus 로고
    • Asymptotic stability properties of θ-methods for the pantograph equation
    • A. Bellen, N. Guglielmi and L. Torelli (1997), 'Asymptotic stability properties of θ-methods for the pantograph equation', Appl. Numer. Math. 24, 275-293.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 275-293
    • Bellen, A.1    Guglielmi, N.2    Torelli, L.3
  • 22
    • 0043232751 scopus 로고    scopus 로고
    • On the contractivity and asymptotic stability of systems of delay differential equations of neutral type
    • A. Bellen, N. Guglielmi and M. Zennaro (1999), 'On the contractivity and asymptotic stability of systems of delay differential equations of neutral type', BIT 39, 1-24.
    • (1999) BIT , vol.39 , pp. 1-24
    • Bellen, A.1    Guglielmi, N.2    Zennaro, M.3
  • 23
    • 84966230115 scopus 로고
    • Natural continuous extensions of Runge-Kutta methods for Volterra integral equations of the second kind and their applications
    • A. Bellen, Z. Jackiewicz, R. Vermiglio and M. Zennaro (1989), 'Natural continuous extensions of Runge-Kutta methods for Volterra integral equations of the second kind and their applications', Math. Comp. 52, 49-63.
    • (1989) Math. Comp. , vol.52 , pp. 49-63
    • Bellen, A.1    Jackiewicz, Z.2    Vermiglio, R.3    Zennaro, M.4
  • 24
    • 0034407032 scopus 로고    scopus 로고
    • Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems
    • A. Bellen and S. Maset (2000), 'Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems', Numer. Math. 84, 351-374.
    • (2000) Numer. Math. , vol.84 , pp. 351-374
    • Bellen, A.1    Maset, S.2
  • 25
    • 0005042142 scopus 로고
    • Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method
    • A. Bellen and M. Zennaro (1985), 'Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method', Numer. Math. 47, 301-316.
    • (1985) Numer. Math. , vol.47 , pp. 301-316
    • Bellen, A.1    Zennaro, M.2
  • 27
    • 0038532342 scopus 로고
    • On the computational solution of differential-difference equations
    • R. Bellman (1963), 'On the computational solution of differential-difference equations', J. Math. Anal. Appl. 2, 108-110.
    • (1963) J. Math. Anal. Appl. , vol.2 , pp. 108-110
    • Bellman, R.1
  • 29
    • 21944450389 scopus 로고    scopus 로고
    • On the solution of an integral-functional equation with a parameter
    • L. Berg and M. Krüppel (1998a), 'On the solution of an integral-functional equation with a parameter', Z. Anal. Anwendungen 17, 159-181.
    • (1998) Z. Anal. Anwendungen , vol.17 , pp. 159-181
    • Berg, L.1    Krüppel, M.2
  • 30
    • 22444454684 scopus 로고    scopus 로고
    • Cantor sets and integral-functional equations
    • L. Berg and M. Krüppel (1998b), 'Cantor sets and integral-functional equations', Z. Anal. Anwendungen 17, 997-1020.
    • (1998) Z. Anal. Anwendungen , vol.17 , pp. 997-1020
    • Berg, L.1    Krüppel, M.2
  • 31
    • 0034509077 scopus 로고    scopus 로고
    • Numerical modelling in biosciences using delay differential equations
    • G. A. Bocharov and F. A. Rihan (2000), 'Numerical modelling in biosciences using delay differential equations', J. Comput. Appl. Math. 125, 183-199.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 183-199
    • Bocharov, G.A.1    Rihan, F.A.2
  • 32
    • 0007028031 scopus 로고
    • Existence, uniqueness, and extendibility of solutions to Volterra integral systems with multiple variable delays
    • J. M. Bownds, J. M. Cushing and R. Schutte (1976), 'Existence, uniqueness, and extendibility of solutions to Volterra integral systems with multiple variable delays', Funkcial. Ekvac. 19, 101-111.
    • (1976) Funkcial. Ekvac. , vol.19 , pp. 101-111
    • Bownds, J.M.1    Cushing, J.M.2    Schutte, R.3
  • 34
    • 2942679580 scopus 로고    scopus 로고
    • Some directions for mathematical epidemiology
    • Dynamical Systems and Their Applications in Biology, Cape Breton 2001 (S. Ruan, G. S. K. Wolkowicz and J. Wu, eds). AMS, Providence, RI
    • F. Brauer and P. van den Driessche (2003), Some directions for mathematical epidemiology, in Dynamical Systems and Their Applications in Biology, Cape Breton 2001 (S. Ruan, G. S. K. Wolkowicz and J. Wu, eds), Vol. 36 of Fields Institute Communications. AMS, Providence, RI, pp. 95-112.
    • (2003) Fields Institute Communications , vol.36 , pp. 95-112
    • Brauer, F.1    Van den Driessche, P.2
  • 35
    • 0002337719 scopus 로고
    • Existence theorems for nonlinear integral equations of Hammerstein type
    • H. Brezis and F. E. Browder (1975), 'Existence theorems for nonlinear integral equations of Hammerstein type', Bull. Amer. Math. Soc. 81, 73-78.
    • (1975) Bull. Amer. Math. Soc. , vol.81 , pp. 73-78
    • Brezis, H.1    Browder, F.E.2
  • 36
    • 84966204227 scopus 로고
    • The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes
    • H. Brunner (1985), 'The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes', Math. Comp. 45, 417-437.
    • (1985) Math. Comp. , vol.45 , pp. 417-437
    • Brunner, H.1
  • 37
    • 38249014608 scopus 로고
    • Implicitly linear collocation methods for nonlinear Volterra integral equations
    • H. Brunner (1992), 'Implicitly linear collocation methods for nonlinear Volterra integral equations'. Appl. Numer. Math. 9, 235-247.
    • (1992) Appl. Numer. Math. , vol.9 , pp. 235-247
    • Brunner, H.1
  • 38
    • 84968494814 scopus 로고
    • Iterated collocation methods for Volterra integral equations with delay arguments
    • H. Brunner (1994a), 'Iterated collocation methods for Volterra integral equations with delay arguments', Math. Comp. 62, 581-599.
    • (1994) Math. Comp. , vol.62 , pp. 581-599
    • Brunner, H.1
  • 39
    • 0005566582 scopus 로고
    • The numerical solution of neutral Volterra integro-differential equations with delay arguments
    • H. Brunner (1994b), 'The numerical solution of neutral Volterra integro-differential equations with delay arguments', Ann. Numer. Math. 1, 309-322.
    • (1994) Ann. Numer. Math. , vol.1 , pp. 309-322
    • Brunner, H.1
  • 40
    • 0002039485 scopus 로고    scopus 로고
    • On the discretization of differential and Volterra integral equations with variable delay
    • H. Brunner (1997a), 'On the discretization of differential and Volterra integral equations with variable delay', BIT 37, 1-12.
    • (1997) BIT , vol.37 , pp. 1-12
    • Brunner, H.1
  • 41
    • 0031210355 scopus 로고    scopus 로고
    • 1896-1996: One hundred years of Volterra integral equations of the first kind
    • H. Brunner (1997b), 1896-1996: One hundred years of Volterra integral equations of the first kind, Appl. Numer. Math. 24, 83-93.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 83-93
    • Brunner, H.1
  • 42
    • 22644449317 scopus 로고    scopus 로고
    • The discretization of neutral functional integro-differential equations by collocation methods
    • H. Brunner (1999a), 'The discretization of neutral functional integro-differential equations by collocation methods', Z. Anal. Anwendungen 18, 393-406.
    • (1999) Z. Anal. Anwendungen , vol.18 , pp. 393-406
    • Brunner, H.1
  • 43
    • 1842565518 scopus 로고    scopus 로고
    • The numerical solution of weakly singular first-kind Volterra integral equations with delay arguments
    • H. Brunner (1999b), 'The numerical solution of weakly singular first-kind Volterra integral equations with delay arguments', Proc. Estonian Acad. Sci. Phys. Math. 48, 90-100.
    • (1999) Proc. Estonian Acad. Sci. Phys. Math. , vol.48 , pp. 90-100
    • Brunner, H.1
  • 44
    • 2942677315 scopus 로고    scopus 로고
    • The discretization of Volterra functional integral equations with proportional delays in Difference and Differential Equations
    • Difference and Differential Equations, Changsha 2002 (S. Elaydi, G. Lada, J. Wu and X. Zou, eds). AMS, Providence, RI. To appear
    • H. Brunner (2004a), 'The discretization of Volterra functional integral equations with proportional delays', in Difference and Differential Equations, Changsha 2002 (S. Elaydi, G. Lada, J. Wu and X. Zou, eds), Vol. 42 of Fields Institute Communications. AMS, Providence, RI. To appear.
    • (2004) Fields Institute Communications , vol.42
    • Brunner, H.1
  • 48
    • 0035541115 scopus 로고    scopus 로고
    • Geometric meshes in collocation methods for Volterra integral equations with proportional delays
    • H. Brunner, Q.-Y. Hu and Q. Lin (2001 a), 'Geometric meshes in collocation methods for Volterra integral equations with proportional delays', IMA J. Numer. Anal. 21, 783-798.
    • (2001) IMA J. Numer. Anal. , vol.21 , pp. 783-798
    • Brunner, H.1    Hu, Q.-Y.2    Lin, Q.3
  • 50
    • 0040575075 scopus 로고    scopus 로고
    • The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
    • H. Brunner, A. Pedas and G. Vainikko (1999), 'The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations', Math. Comp. 68, 1079-1095.
    • (1999) Math. Comp. , vol.68 , pp. 1079-1095
    • Brunner, H.1    Pedas, A.2    Vainikko, G.3
  • 51
    • 0035382421 scopus 로고    scopus 로고
    • Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels
    • H. Brunner, A. Pedas and G. Vainikko (2001b), 'Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels', SIAM J. Numer. Anal. 39, 957-982.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 957-982
    • Brunner, H.1    Pedas, A.2    Vainikko, G.3
  • 52
    • 0346272624 scopus 로고    scopus 로고
    • Stability of solutions of neutral functional integro-differential equations and their discretizations
    • H. Brunner and R. Vermiglio (2003). 'Stability of solutions of neutral functional integro-differential equations and their discretizations', Computing 71, 229-245.
    • (2003) Computing , vol.71 , pp. 229-245
    • Brunner, H.1    Vermiglio, R.2
  • 53
    • 2942657703 scopus 로고    scopus 로고
    • Primary discontinuities in solutions for delay integro-differential equations
    • H. Brunner and W. Zhang (1999), 'Primary discontinuities in solutions for delay integro-differential equations', Methods Appl. Anal. 6, 525-533.
    • (1999) Methods Appl. Anal. , vol.6 , pp. 525-533
    • Brunner, H.1    Zhang, W.2
  • 54
    • 0342489541 scopus 로고
    • Numerical analysis of functional differential equations with a variable delay
    • Numerical Analysis, Dundee 1991 (D. F. Griffiths and G. A. Watson, eds), Longman, Harlow
    • M. Buhmann and A. Iserles (1991), 'Numerical analysis of functional differential equations with a variable delay', in Numerical Analysis, Dundee 1991 (D. F. Griffiths and G. A. Watson, eds), Vol. 260 of Pitman Research Notes in Mathematics Series, Longman, Harlow, pp. 17-33.
    • (1991) Pitman Research Notes in Mathematics Series , vol.260 , pp. 17-33
    • Buhmann, M.1    Iserles, A.2
  • 55
    • 0038948786 scopus 로고
    • On the dynamics of a discretized neutral equation
    • M. Buhmann and A. Iserles (1992), 'On the dynamics of a discretized neutral equation', IMA J. Numer. Anal. 12, 339-363.
    • (1992) IMA J. Numer. Anal. , vol.12 , pp. 339-363
    • Buhmann, M.1    Iserles, A.2
  • 56
    • 84968503713 scopus 로고
    • Stability of the discretized pantograph differential equation
    • M. Buhmann and A. Iserles (1993), 'Stability of the discretized pantograph differential equation', Math. Comp. 60, 575-589.
    • (1993) Math. Comp. , vol.60 , pp. 575-589
    • Buhmann, M.1    Iserles, A.2
  • 57
    • 0040132997 scopus 로고
    • Runge-Kutta methods for neutral differential equations
    • R. P. Agarwal, ed., World Scientific, River Edge, NJ
    • M. Buhmann, A. Iserles and S. P. Nørsett (1993), 'Runge-Kutta methods for neutral differential equations', in Contributions in Numerical Mathematics, Singapore 1993 (R. P. Agarwal, ed.), World Scientific, River Edge, NJ, pp. 85-98.
    • (1993) Contributions in Numerical Mathematics, Singapore 1993 , pp. 85-98
    • Buhmann, M.1    Iserles, A.2    Nørsett, S.P.3
  • 58
    • 2942696555 scopus 로고
    • Dissertation, Fakultät für Mathematik, Ludwig-Maximilians-Universität München
    • A. Burgstaller (1993), Kollokationsverfahren für Anfangswertprobleme, Dissertation, Fakultät für Mathematik, Ludwig-Maximilians-Universität München.
    • (1993) Kollokationsverfahren für Anfangswertprobleme
    • Burgstaller, A.1
  • 59
    • 2942675139 scopus 로고    scopus 로고
    • A modified collocation method for Volterra delay integro-differential equations with multiple delays
    • R. P. Agarwal and D. O'Regan, eds, Gordon and Breach, Amsterdam
    • A. Burgstaller (2000), 'A modified collocation method for Volterra delay integro-differential equations with multiple delays', in Integral and Integro-differential Equations: Theory, Methods and Applications (R. P. Agarwal and D. O'Regan, eds), Gordon and Breach, Amsterdam, pp. 39-53.
    • (2000) Integral and Integro-differential Equations: Theory, Methods and Applications , pp. 39-53
    • Burgstaller, A.1
  • 62
    • 0002115425 scopus 로고
    • Linear functional differential equations as semigroups on product spaces
    • J. A. Burns, T. L. Herdman and H. W. Stech (1983c), 'Linear functional differential equations as semigroups on product spaces', SIAM J. Math. Anal. 14, 98-116.
    • (1983) SIAM J. Math. Anal. , vol.14 , pp. 98-116
    • Burns, J.A.1    Herdman, T.L.2    Stech, H.W.3
  • 64
    • 38249020396 scopus 로고
    • Neutral functional integro-differential equations with weakly singular kernels
    • J. A. Burns, T. L. Herdman and J. Turi (1990), 'Neutral functional integro-differential equations with weakly singular kernels', J. Math. Anal. Appl. 145, 371-401.
    • (1990) J. Math. Anal. Appl. , vol.145 , pp. 371-401
    • Burns, J.A.1    Herdman, T.L.2    Turi, J.3
  • 66
    • 0019194059 scopus 로고
    • The effect of integral conditions in certain equations modelling epidemics and population growth
    • S. Busenberg and K. L. Cooke (1980), 'The effect of integral conditions in certain equations modelling epidemics and population growth', J. Math. Biol. 10, 13-32.
    • (1980) J. Math. Biol. , vol.10 , pp. 13-32
    • Busenberg, S.1    Cooke, K.L.2
  • 67
    • 38249017097 scopus 로고
    • On the numerical stability of Volterra integral equations with delay arguments
    • B. Cahlon (1990), 'On the numerical stability of Volterra integral equations with delay arguments', J. Comput. Appl. Math. 33, 97-104.
    • (1990) J. Comput. Appl. Math. , vol.33 , pp. 97-104
    • Cahlon, B.1
  • 68
    • 38249013865 scopus 로고
    • Numerical solutions for functional integral equations with state-dependent delay
    • B. Cahlon (1992), 'Numerical solutions for functional integral equations with state-dependent delay', Appl. Numer. Math. 9, 291-305.
    • (1992) Appl. Numer. Math. , vol.9 , pp. 291-305
    • Cahlon, B.1
  • 69
    • 0343358917 scopus 로고
    • On the stability of Volterra integral equations with a lagging argument
    • B. Cahlon (1995), 'On the stability of Volterra integral equations with a lagging argument', BIT 35, 19-29.
    • (1995) BIT , vol.35 , pp. 19-29
    • Cahlon, B.1
  • 70
    • 0022247079 scopus 로고
    • Numerical solutions of Volterra integral equations with a solution dependent delay
    • B. Cahlon and L. J. Nachman (1985), 'Numerical solutions of Volterra integral equations with a solution dependent delay', J. Math. Anal. Appl. 112, 541-562.
    • (1985) J. Math. Anal. Appl. , vol.112 , pp. 541-562
    • Cahlon, B.1    Nachman, L.J.2
  • 71
    • 0021519461 scopus 로고
    • Numerical solution of Volterra integral equations with delay arguments
    • B. Cahlon, L. J. Nachman and D. Schmidt (1984), 'Numerical solution of Volterra integral equations with delay arguments', J. Integral Equations 7, 191-208.
    • (1984) J. Integral Equations , vol.7 , pp. 191-208
    • Cahlon, B.1    Nachman, L.J.2    Schmidt, D.3
  • 72
    • 0031245310 scopus 로고    scopus 로고
    • Stability criteria for certain delay integral equations of Volterra type
    • B. Cahlon and D. Schmidt (1997), 'Stability criteria for certain delay integral equations of Volterra type', J. Comput. Appl. Math. 84, 161-188.
    • (1997) J. Comput. Appl. Math. , vol.84 , pp. 161-188
    • Cahlon, B.1    Schmidt, D.2
  • 73
    • 0343552049 scopus 로고
    • Methods of upper and lower solutions for non-linear delay integral equations modelling epidemics and population growth
    • A. Cañada and A. Zertiti (1994), 'Methods of upper and lower solutions for non-linear delay integral equations modelling epidemics and population growth', Math. Models Methods Appl. Sci. 4, 107-119.
    • (1994) Math. Models Methods Appl. Sci. , vol.4 , pp. 107-119
    • Cañada, A.1    Zertiti, A.2
  • 74
    • 84971116385 scopus 로고
    • The functional differential equation y′(x) = ay(λx) + by(x)
    • J. Carr and J. Dyson (1976), 'The functional differential equation y′(x) = ay(λx) + by(x)', Proc. Roy. Soc. Edinburgh Sect. A 74, 5-22.
    • (1976) Proc. Roy. Soc. Edinburgh Sect. A , vol.74 , pp. 5-22
    • Carr, J.1    Dyson, J.2
  • 75
    • 0039448181 scopus 로고    scopus 로고
    • Collapsible backward continuation and numerical approximations in a functional differential equation
    • L. A. V. Carvalho and K. L. Cooke (1998). 'Collapsible backward continuation and numerical approximations in a functional differential equation'. J. Differential Equations 143, 96-109.
    • (1998) J. Differential Equations , vol.143 , pp. 96-109
    • Carvalho, L.A.V.1    Cooke, K.L.2
  • 76
    • 0007131918 scopus 로고
    • On some linear Volterra delay equations
    • J. Cerha (1976), 'On some linear Volterra delay equations', Časopis Pěst. Mat. 101, 111-123.
    • (1976) Časopis Pěst. Mat. , vol.101 , pp. 111-123
    • Cerha, J.1
  • 77
    • 0007126845 scopus 로고
    • λx g(x,y, f(y))dy
    • λx g(x,y, f(y))dy', Internat. J. Math. Math. Sci. 14, 27-44.
    • (1990) Internat. J. Math. Math. Sci. , vol.14 , pp. 27-44
  • 78
    • 25044436829 scopus 로고    scopus 로고
    • An analytic semigroup setting for a class of Volterra equations
    • P. Clément, W. Desch and K. W. Homan (2002), 'An analytic semigroup setting for a class of Volterra equations'. J. Integral Equations Appl. 14, 239-281.
    • (2002) J. Integral Equations Appl. , vol.14 , pp. 239-281
    • Clément, P.1    Desch, W.2    Homan, K.W.3
  • 79
    • 0017120521 scopus 로고
    • An epidemic equation with immigration
    • K. L. Cooke (1976), 'An epidemic equation with immigration', Math. Biosci. 29, 135-158.
    • (1976) Math. Biosci. , vol.29 , pp. 135-158
    • Cooke, K.L.1
  • 80
    • 0017104702 scopus 로고
    • A periodicity threshold theorem for epidemics and population growth
    • K. L. Cooke and J. L. Kaplan (1976), 'A periodicity threshold theorem for epidemics and population growth', Math. Biosci. 31, 87-104.
    • (1976) Math. Biosci. , vol.31 , pp. 87-104
    • Cooke, K.L.1    Kaplan, J.L.2
  • 81
    • 25644446425 scopus 로고
    • Some equations modelling growth processes and epidemics
    • K. L. Cooke and J.A. Yorke (1973), 'Some equations modelling growth processes and epidemics', Math. Biosci. 16, 75-101.
    • (1973) Math. Biosci. , vol.16 , pp. 75-101
    • Cooke, K.L.1    Yorke, J.A.2
  • 82
    • 85025379787 scopus 로고
    • Equations with unbounded delay: A survey
    • C. Corduneanu and V. Lakshmikantham (1980), 'Equations with unbounded delay: a survey', Nonlinear Anal. 4, 831-877.
    • (1980) Nonlinear Anal. , vol.4 , pp. 831-877
    • Corduneanu, C.1    Lakshmikantham, V.2
  • 85
    • 0015315774 scopus 로고
    • The numerical solution of Volterra functional differential equations by Euler's method
    • C. W. Cryer and L. Tavernini (1972). 'The numerical solution of Volterra functional differential equations by Euler's method', SIAM J. Numer. Anal. 9, 105-129.
    • (1972) SIAM J. Numer. Anal. , vol.9 , pp. 105-129
    • Cryer, C.W.1    Tavernini, L.2
  • 88
    • 0038950460 scopus 로고
    • On a special Volterra integral equation of the first kind
    • A. M. Denisov and A. Lorenzi (1995), 'On a special Volterra integral equation of the first kind', Boll. Un. Mat. Ital. B 9, 443-457.
    • (1995) Boll. Un. Mat. Ital. B , vol.9 , pp. 443-457
    • Denisov, A.M.1    Lorenzi, A.2
  • 89
    • 2942677317 scopus 로고    scopus 로고
    • Existence results and regularization techniques for severely ill-posed integrofunctional equations
    • A. M. Denisov and A. Lorenzi (1997). 'Existence results and regularization techniques for severely ill-posed integrofunctional equations', Boll. Un. Mat. Ital. B 11, 713-732.
    • (1997) Boll. Un. Mat. Ital. B , vol.11 , pp. 713-732
    • Denisov, A.M.1    Lorenzi, A.2
  • 90
    • 0010890110 scopus 로고
    • Kato problem for functional-differential equations and difference Schrödinger operators
    • Order, Disorder and Chaos in Quantum Systems, Dubna 1989 (P. Exner and H. Neidhardt. eds)
    • G. A. Derfel (1990), 'Kato problem for functional-differential equations and difference Schrödinger operators', in Order, Disorder and Chaos in Quantum Systems, Dubna 1989 (P. Exner and H. Neidhardt. eds), Oper. Theory Adv. Appl. 46, 319-321.
    • (1990) Oper. Theory Adv. Appl. , vol.46 , pp. 319-321
    • Derfel, G.A.1
  • 91
    • 2942657700 scopus 로고
    • Functional differential equations with linearly transformed arguments and their applications
    • C. Perelló et al., eds, World Scientific, River Edge, NJ
    • G. A. Derfel (1991), 'Functional differential equations with linearly transformed arguments and their applications', in Proc. EQUADIFF 91, Barcelona 1991 (C. Perelló et al., eds), World Scientific, River Edge, NJ, pp. 421-423.
    • (1991) Proc. EQUADIFF 91, Barcelona 1991 , pp. 421-423
    • Derfel, G.A.1
  • 92
    • 2942631469 scopus 로고
    • Spectral methods in the theory of differential-functional equations
    • G. A. Derfel and S. A. Molchanov (1990), 'Spectral methods in the theory of differential-functional equations', Math. Notes Acad. Sci. USSR 47, 254-260.
    • (1990) Math. Notes Acad. Sci. USSR , vol.47 , pp. 254-260
    • Derfel, G.A.1    Molchanov, S.A.2
  • 93
    • 0040821594 scopus 로고    scopus 로고
    • On the asymptotics of solutions of a class of linear functional-differential equations
    • G. A. Derfel and F. Vogl (1996), 'On the asymptotics of solutions of a class of linear functional-differential equations', Europ. J. Appl. Math. 7, 511-518.
    • (1996) Europ. J. Appl. Math , vol.7 , pp. 511-518
    • Derfel, G.A.1    Vogl, F.2
  • 97
    • 0036627555 scopus 로고    scopus 로고
    • Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations
    • K. Engelborghs and E. Doedel (2002), 'Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations', Numer. Math. 91, 627-648.
    • (2002) Numer. Math. , vol.91 , pp. 627-648
    • Engelborghs, K.1    Doedel, E.2
  • 98
    • 0034770393 scopus 로고    scopus 로고
    • Collocation methods for the computation of periodic solutions of delay differential equations
    • K. Engelborghs, T. Luzyanina, K. J. in 't Hout and D. Roose (2000), 'Collocation methods for the computation of periodic solutions of delay differential equations', SIAM J. Sci. Comput. 22, 1593-1609.
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 1593-1609
    • Engelborghs, K.1    Luzyanina, T.2    In 'T Hout, K.J.3    Roose, D.4
  • 99
    • 0001080457 scopus 로고    scopus 로고
    • Convergence analysis of the solution of retarded and neutral delay differential equations by continuous numerical methods
    • W. H. Enright and H. Hayashi (1998), 'Convergence analysis of the solution of retarded and neutral delay differential equations by continuous numerical methods', SIAM J. Numer. Anal. 35, 572-585.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 572-585
    • Enright, W.H.1    Hayashi, H.2
  • 100
    • 0031212295 scopus 로고    scopus 로고
    • Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay
    • W. H. Enright and M. Hu (1997), 'Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay', Appl. Numer. Math. 24, 175-190.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 175-190
    • Enright, W.H.1    Hu, M.2
  • 102
    • 2942672927 scopus 로고
    • Numerische Behandlung einer Volterraschen Integralgleichung
    • R. Esser (1978), 'Numerische Behandlung einer Volterraschen Integralgleichung', Computing 19, 269-284.
    • (1978) Computing , vol.19 , pp. 269-284
    • Esser, R.1
  • 103
    • 0040047326 scopus 로고
    • Embedding of delay equations into an infinite-dimensional ODE system
    • A. Feldstein, A. Iserles and D. Levin (1995), 'Embedding of delay equations into an infinite-dimensional ODE system', J. Differential Equations 117, 127-150.
    • (1995) J. Differential Equations , vol.117 , pp. 127-150
    • Feldstein, A.1    Iserles, A.2    Levin, D.3
  • 104
    • 22044440742 scopus 로고    scopus 로고
    • On neutral functional-differential equations with variable time delays
    • A. Feldstein and Y. Liu (1998), 'On neutral functional-differential equations with variable time delays', Math. Proc. Cambridge Phil. Soc. 124, 371-384.
    • (1998) Math. Proc. Cambridge Phil. Soc. , vol.124 , pp. 371-384
    • Feldstein, A.1    Liu, Y.2
  • 105
    • 0040300133 scopus 로고
    • High order methods for state-dependent delay differential equations with nonsmooth solutions
    • A. Feldstein and K. W. Neves (1984), 'High order methods for state-dependent delay differential equations with nonsmooth solutions', SIAM J. Numer. Anal. 21, 844-863.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 844-863
    • Feldstein, A.1    Neves, K.W.2
  • 108
    • 0010822964 scopus 로고
    • Dirichlet solutions for certain functional differential equations
    • Japan-United States Seminar on Ordinary Differential and Functional Equations, Kyoto 1971 (M. Urabe, ed.), Springer, Berlin/Heidelberg
    • P. O. Frederickson (1971), 'Dirichlet solutions for certain functional differential equations', in Japan-United States Seminar on Ordinary Differential and Functional Equations, Kyoto 1971 (M. Urabe, ed.). Vol. 243 of Lecture Notes in Mathematics, Springer, Berlin/Heidelberg, pp. 249-251.
    • (1971) Lecture Notes in Mathematics , vol.243 , pp. 249-251
    • Frederickson, P.O.1
  • 109
    • 2942638172 scopus 로고
    • Smoothness of solutions of functional differential equations
    • M. de Gee (1985), 'Smoothness of solutions of functional differential equations', J. Math. Anal. Appl. 107, 103-121.
    • (1985) J. Math. Anal. Appl. , vol.107 , pp. 103-121
    • De Gee, M.1
  • 110
    • 2942644777 scopus 로고
    • Perturbation theory for Volterra integro-differential systems
    • S. I. Grossman and R. K. Miller (1970), 'Perturbation theory for Volterra integro-differential systems', J. Differential Equations 8, 457-474.
    • (1970) J. Differential Equations , vol.8 , pp. 457-474
    • Grossman, S.I.1    Miller, R.K.2
  • 111
    • 0039835397 scopus 로고    scopus 로고
    • Delay dependent stability regions of θ-methods for delay differential equations
    • N. Guglielmi (1998), 'Delay dependent stability regions of θ-methods for delay differential equations'. IMA J. Numer. Anal. 18, 399-418.
    • (1998) IMA J. Numer. Anal. , vol.18 , pp. 399-418
    • Guglielmi, N.1
  • 112
    • 0035529769 scopus 로고    scopus 로고
    • Geometric proofs of numerical stability for delay differential equations
    • N. Guglielmi and E. Hairer (2001a), 'Geometric proofs of numerical stability for delay differential equations', IMA J. Numer. Anal. 21, 439-450.
    • (2001) IMA J. Numer. Anal. , vol.21 , pp. 439-450
    • Guglielmi, N.1    Hairer, E.2
  • 113
    • 0034891830 scopus 로고    scopus 로고
    • Implementing Radau IIA methods for stiff delay differential equations
    • N. Guglielmi and E. Hairer (2001b), 'Implementing Radau IIA methods for stiff delay differential equations'. Computing 67, 1-12.
    • (2001) Computing , vol.67 , pp. 1-12
    • Guglielmi, N.1    Hairer, E.2
  • 114
    • 0038166019 scopus 로고    scopus 로고
    • Stability of one-leg θ-methods for the variable coefficient pantograph equation on the quasi-geometric mesh
    • N. Guglielmi and M. Zennaro (2003), 'Stability of one-leg θ-methods for the variable coefficient pantograph equation on the quasi-geometric mesh', IMA J. Numer. Anal. 23, 421-438.
    • (2003) IMA J. Numer. Anal. , vol.23 , pp. 421-438
    • Guglielmi, N.1    Zennaro, M.2
  • 115
    • 0036853277 scopus 로고    scopus 로고
    • Numerical approximation of neutral differential equations on infinite intervals
    • I. Györi and F. Härtung (2002), 'Numerical approximation of neutral differential equations on infinite intervals', J. Differential Equations Appl. 8, 983-999.
    • (2002) J. Differential Equations Appl. , vol.8 , pp. 983-999
    • Györi, I.1    Härtung, F.2
  • 116
    • 0002078163 scopus 로고
    • Numerical approximations for a class of differential equations with time- and state-dependent delays
    • I. Györi, F. Härtung and J. Turi (1995), 'Numerical approximations for a class of differential equations with time- and state-dependent delays', Appl. Math. Lett. 8, 19-24.
    • (1995) Appl. Math. Lett. , vol.8 , pp. 19-24
    • Györi, I.1    Härtung, F.2    Turi, J.3
  • 117
    • 0000907709 scopus 로고    scopus 로고
    • Preservation of stability in delay equations under delay perturbations
    • I. Györi, F. Härtung and J. Turi (1998), 'Preservation of stability in delay equations under delay perturbations', J. Math. Anal. Appl. 220, 290-312.
    • (1998) J. Math. Anal. Appl. , vol.220 , pp. 290-312
    • Györi, I.1    Härtung, F.2    Turi, J.3
  • 119
    • 0005523252 scopus 로고
    • Some new results and problems in the theory of functional-differential equations
    • A. Halanay and J. A. Yorke (1971), 'Some new results and problems in the theory of functional-differential equations, SIAM Review 13, 5-80.
    • (1971) SIAM Review , vol.13 , pp. 5-80
    • Halanay, A.1    Yorke, J.A.2
  • 122
    • 0031210356 scopus 로고    scopus 로고
    • On existence, uniqueness and numerical approximation for neutral equations with state-dependent delay
    • F. Hartung, T. L. Herdman and J. Turi (1997), 'On existence, uniqueness and numerical approximation for neutral equations with state-dependent delay', Appl. Numer. Math. 24, 393-409.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 393-409
    • Hartung, F.1    Herdman, T.L.2    Turi, J.3
  • 123
    • 0001015107 scopus 로고
    • On the asymptotic behavior of the solutions of a state-dependent differential equation
    • F. Hartung and J. Turi (1995). 'On the asymptotic behavior of the solutions of a state-dependent differential equation', Differential Integral Equations 8, 1867-1872.
    • (1995) Differential Integral Equations , vol.8 , pp. 1867-1872
    • Hartung, F.1    Turi, J.2
  • 124
    • 21744432249 scopus 로고    scopus 로고
    • Numerical treatment of retarded differential-algebraic equations by collocation methods
    • R. Hauber (1997), 'Numerical treatment of retarded differential-algebraic equations by collocation methods', Adv. Comput. Math. 7, 573-592.
    • (1997) Adv. Comput. Math. , vol.7 , pp. 573-592
    • Hauber, R.1
  • 125
    • 2942651025 scopus 로고
    • Functional differential equations with discontinuous right-hand side
    • S. O. Londen and O. J. Staffans, eds, Springer, Berlin
    • T. L. Herdman and J. A. Burns (1979), 'Functional differential equations with discontinuous right-hand side', in Volterra Equations, Otaniemi 1978 (S. O. Londen and O. J. Staffans, eds), Springer, Berlin, pp. 99-106.
    • (1979) Volterra Equations, Otaniemi 1978 , pp. 99-106
    • Herdman, T.L.1    Burns, J.A.2
  • 126
    • 2942640336 scopus 로고
    • An application of finite Hilbert transforms in the derivation of a state space model for an aeroelastic system
    • T. L. Herdman and J. Turi (1991), 'An application of finite Hilbert transforms in the derivation of a state space model for an aeroelastic system', J. Integral Equations Appl. 3, 271-287.
    • (1991) J. Integral Equations Appl. , vol.3 , pp. 271-287
    • Herdman, T.L.1    Turi, J.2
  • 127
    • 0029445684 scopus 로고
    • An SIS epidemic model with variable population size and a delay
    • H. W. Hethcote and P. van den Driessche (1995), 'An SIS epidemic model with variable population size and a delay', J. Math. Biol. 34, 177-194.
    • (1995) J. Math. Biol. , vol.34 , pp. 177-194
    • Hethcote, H.W.1    Van den Driessche, P.2
  • 128
  • 129
    • 0024578161 scopus 로고
    • An epidemiological model with a delay and a nonlinear incidence rate
    • H. W. Hethcote, M. A. Lewis and P. van den Driessche (1989), 'An epidemiological model with a delay and a nonlinear incidence rate', J. Math. Biol. 27, 49-64.
    • (1989) J. Math. Biol. , vol.27 , pp. 49-64
    • Hethcote, H.W.1    Lewis, M.A.2    Van den Driessche, P.3
  • 130
    • 0018856876 scopus 로고
    • Integral equation models for endemic infectious diseases
    • H. W. Hethcote and D. W. Tudor (1980), 'Integral equation models for endemic infectious diseases', J. Math. Biol. 9, 37-47.
    • (1980) J. Math. Biol. , vol.9 , pp. 37-47
    • Hethcote, H.W.1    Tudor, D.W.2
  • 131
    • 34249839190 scopus 로고
    • A new interpolation procedure for adapting Runge-kutta methods to delay differential equations
    • K. J. in 't Hout (1992), 'A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations', BIT 32, 634-649.
    • (1992) BIT , vol.32 , pp. 634-649
    • In 'T Hout, K.J.1
  • 133
    • 2942659962 scopus 로고    scopus 로고
    • Stepwise collocation methods based on the high-order interpolation for Volterra integral equations with multiple delays
    • in Chinese
    • Q.-Y. Hu (1997), 'Stepwise collocation methods based on the high-order interpolation for Volterra integral equations with multiple delays' (in Chinese), Math. Numer. Sinica 19, 353-358.
    • (1997) Math. Numer. Sinica , vol.19 , pp. 353-358
    • Hu, Q.-Y.1
  • 134
    • 0039491179 scopus 로고    scopus 로고
    • Geometric meshes and their application to Volterra integro-differential equations with singularities
    • Q.-Y. Hu (1998), 'Geometric meshes and their application to Volterra integro-differential equations with singularities', IMA J. Numer, Anal. 18, 151-164.
    • (1998) IMA J. Numer, Anal. , vol.18 , pp. 151-164
    • Hu, Q.-Y.1
  • 135
    • 0033208056 scopus 로고    scopus 로고
    • Multilevel correction for discrete collocation solutions of Volterra integral equations with delay arguments
    • Q.-Y. Hu (1999), 'Multilevel correction for discrete collocation solutions of Volterra integral equations with delay arguments', Appl. Numer. Math. 31, 159-171.
    • (1999) Appl. Numer. Math. , vol.31 , pp. 159-171
    • Hu, Q.-Y.1
  • 136
    • 2942692227 scopus 로고    scopus 로고
    • Multilevel correction for collocation solutions of Volterra delay integro-differential equations
    • Q.-Y. Hu and L. Peng (1999), 'Multilevel correction for collocation solutions of Volterra delay integro-differential equations' (in Chinese), Systems Sci. Math. Sci. 19, 134-141.
    • (1999) Systems Sci. Math. Sci. , vol.19 , pp. 134-141
    • Hu, Q.-Y.1    Peng, L.2
  • 137
    • 52649085452 scopus 로고
    • On the generalized pantograph functional differential equation
    • A. Iserles (1993), 'On the generalized pantograph functional differential equation', Europ. J. Appl. Math. 4, 1-38.
    • (1993) Europ. J. Appl. Math. , vol.4 , pp. 1-38
    • Iserles, A.1
  • 138
    • 0242709242 scopus 로고
    • Numerical analysis of delay differential equations with variable delays
    • A. Iserles (1994a), 'Numerical analysis of delay differential equations with variable delays', Ann. Numer. Math. 1, 133-152.
    • (1994) Ann. Numer. Math. , vol.1 , pp. 133-152
    • Iserles, A.1
  • 139
    • 0000427731 scopus 로고
    • On nonlinear delay-differential equations
    • A. Iserles (1994b), 'On nonlinear delay-differential equations', Trans. Amer. Math. Soc. 344, 441-477.
    • (1994) Trans. Amer. Math. Soc. , vol.344 , pp. 441-477
    • Iserles, A.1
  • 140
    • 0039541346 scopus 로고
    • The asymptotic behaviour of certain difference equations with proportional delay
    • A. Iserles (1994c), 'The asymptotic behaviour of certain difference equations with proportional delay', Comput. Math. Appl. 28, 141-152.
    • (1994) Comput. Math. Appl. , vol.28 , pp. 141-152
    • Iserles, A.1
  • 141
    • 0003247776 scopus 로고    scopus 로고
    • Beyond the classical theory of computational ODEs
    • I. S. Duff and G. A. Watson, eds, Clarendon Press, Oxford
    • A. Iserles (1997a), 'Beyond the classical theory of computational ODEs', in The State of the Art in Numerical Analysis, York 1996 (I. S. Duff and G. A. Watson, eds), Clarendon Press, Oxford, pp. 171-192.
    • (1997) The State of the Art in Numerical Analysis, York 1996 , pp. 171-192
    • Iserles, A.1
  • 142
    • 0031212296 scopus 로고    scopus 로고
    • Exact and discretized stability of the pantograph equation
    • A. Iserles (1997b), 'Exact and discretized stability of the pantograph equation', Appl. Numer. Math. 24, 295-308.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 295-308
    • Iserles, A.1
  • 143
    • 84893735286 scopus 로고
    • On pantograph integro-differential equations
    • A. Iserles and Y. Liu (1994), 'On pantograph integro-differential equations', J. Integral Equations Appl. 6, 213-237.
    • (1994) J. Integral Equations Appl. , vol.6 , pp. 213-237
    • Iserles, A.1    Liu, Y.2
  • 144
    • 0031081849 scopus 로고    scopus 로고
    • On neutral functional-differential equations with proportional delays
    • A. Iserles and Y. Liu (1997), 'On neutral functional-differential equations with proportional delays', J. Math. Anal. Appl. 207, 73-95.
    • (1997) J. Math. Anal. Appl. , vol.207 , pp. 73-95
    • Iserles, A.1    Liu, Y.2
  • 145
    • 0009028686 scopus 로고
    • Stability and asymptotic stability of functional-differential equations
    • A. Iserles and J. Terjéki (1995), 'Stability and asymptotic stability of functional-differential equations', J. London Math. Soc. 51, 559-572.
    • (1995) J. London Math. Soc. , vol.51 , pp. 559-572
    • Iserles, A.1    Terjéki, J.2
  • 146
    • 0000826399 scopus 로고    scopus 로고
    • On the attainable order of collocation methods for the neutral functional-differential equations with proportional delays
    • E. Ishiwata (2000), 'On the attainable order of collocation methods for the neutral functional-differential equations with proportional delays', Computing 64, 207-222.
    • (2000) Computing , vol.64 , pp. 207-222
    • Ishiwata, E.1
  • 147
    • 2942633669 scopus 로고
    • Approximation of infinite delay and Volterra type equations
    • K. Ito and F. Kappel (1989), 'Approximation of infinite delay and Volterra type equations', Numer. Math. 54, 405-444.
    • (1989) Numer. Math. , vol.54 , pp. 405-444
    • Ito, K.1    Kappel, F.2
  • 148
    • 0011541435 scopus 로고
    • On integro-differential equations with weakly singular kernels
    • Differential Equations with Applications (J. A. Goldstein et al., eds), Marcel Dekker, New York
    • K. Ito and F. Kappel (1991), 'On integro-differential equations with weakly singular kernels', in Differential Equations with Applications (J. A. Goldstein et al., eds), Vol. 133 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York. pp. 209-218.
    • (1991) Lecture Notes in Pure and Applied Mathematics , vol.133 , pp. 209-218
    • Ito, K.1    Kappel, F.2
  • 150
    • 0030577719 scopus 로고    scopus 로고
    • On well-posedness of singular neutral equations in the state space C
    • K. Ito, F. Kappel and J. Turi (1996), 'On well-posedness of singular neutral equations in the state space C', J. Differential Equations 125, 40-72.
    • (1996) J. Differential Equations , vol.125 , pp. 40-72
    • Ito, K.1    Kappel, F.2    Turi, J.3
  • 151
    • 0026374092 scopus 로고
    • Numerical methods for a class of singular integro-differential equations based on semigroup approximation
    • K. Ito and J. Turi (1991). 'Numerical methods for a class of singular integro-differential equations based on semigroup approximation', SIAM J. Numer. Anal. 28, 1698-1722.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1698-1722
    • Ito, K.1    Turi, J.2
  • 152
    • 0021448666 scopus 로고
    • One-step methods of any order for neutral functional differential equations
    • Z. Jackiewicz (1984), 'One-step methods of any order for neutral functional differential equations', SIAM J. Numer. Anal. 21, 486-511.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 486-511
    • Jackiewicz, Z.1
  • 153
    • 0005303333 scopus 로고
    • The numerical solution of functional differential equations
    • Z. Jackiewicz and M. Kwapisz (1991), 'The numerical solution of functional differential equations', Mat. Stos. 33, 57-78.
    • (1991) Mat. Stos. , vol.33 , pp. 57-78
    • Jackiewicz, Z.1    Kwapisz, M.2
  • 154
    • 0040278321 scopus 로고
    • Spline approximations for neutral functional differential equations
    • F. Kappel and K. Kunisch (1981), 'Spline approximations for neutral functional differential equations'. SIAM J. Numer. Anal. 18, 1058-1080.
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 1058-1080
    • Kappel, F.1    Kunisch, K.2
  • 155
    • 84966257202 scopus 로고
    • Invariance results for delay and Volterra equations in fractional order Sobolev space
    • F. Kappel and K. Kunisch (1987), 'Invariance results for delay and Volterra equations in fractional order Sobolev space', Trans. Amer. Math. Soc. 304, 1-51.
    • (1987) Trans. Amer. Math. Soc. , vol.304 , pp. 1-51
    • Kappel, F.1    Kunisch, K.2
  • 156
    • 0022659425 scopus 로고
    • On neutral functional differential equations with nonatomic difference operator
    • F. Kappel and K. P. Zhang (1986), 'On neutral functional differential equations with nonatomic difference operator', J. Math. Anal. Appl. 113, 311-343.
    • (1986) J. Math. Anal. Appl. , vol.113 , pp. 311-343
    • Kappel, F.1    Zhang, K.P.2
  • 157
    • 38149143519 scopus 로고
    • Computer solutions of state-dependent delay differential equations
    • A. Karoui and R. Vaillancourt (1994), 'Computer solutions of state-dependent delay differential equations', Comput. Math. Appl. 27, 37-51.
    • (1994) Comput. Math. Appl. , vol.27 , pp. 37-51
    • Karoui, A.1    Vaillancourt, R.2
  • 159
    • 84966219417 scopus 로고
    • The functional-differential equation y′(x) = ay(λx] + by(x)
    • T. Kato and J. B. McLeod (1971), 'The functional-differential equation y′(x) = ay(λx] + by(x)', Bull. Amer. Math. Soc. 77, 891-937.
    • (1971) Bull. Amer. Math. Soc. , vol.77 , pp. 891-937
    • Kato, T.1    McLeod, J.B.2
  • 160
    • 0039329165 scopus 로고    scopus 로고
    • Continuous collocation approximations to solutions of first kind Volterra equations
    • J.-P. Kauthen and H. Brunner (1997), 'Continuous collocation approximations to solutions of first kind Volterra equations', Math. Comp. 66, 1441-1459.
    • (1997) Math. Comp. , vol.66 , pp. 1441-1459
    • Kauthen, J.-P.1    Brunner, H.2
  • 161
    • 2142727446 scopus 로고
    • An approximate solution of the initial value problem for integro-differential equations with a deviating argument
    • N. G. Kazakova and D. D. Bainov (1990), 'An approximate solution of the initial value problem for integro-differential equations with a deviating argument', Math. J. Toyama Univ. 13, 9-27.
    • (1990) Math. J. Toyama Univ. , vol.13 , pp. 9-27
    • Kazakova, N.G.1    Bainov, D.D.2
  • 163
    • 22844457024 scopus 로고    scopus 로고
    • Stability of Runge-Kutta methods for the generalized pantograph equation
    • T. Koto (1999). 'Stability of Runge-Kutta methods for the generalized pantograph equation', Numer. Math. 84, 233-247.
    • (1999) Numer. Math. , vol.84 , pp. 233-247
    • Koto, T.1
  • 164
    • 0037102575 scopus 로고    scopus 로고
    • Stability of Runge-Kutta methods for delay integro-differential equations
    • T. Koto (2002), 'Stability of Runge-Kutta methods for delay integro-differential equations', J. Comput. Appl. Math. 145, 483-492.
    • (2002) J. Comput. Appl. Math. , vol.145 , pp. 483-492
    • Koto, T.1
  • 166
    • 0001255506 scopus 로고
    • Monotonic and oscillatory solutions of a linear neutral delay equation with infinite lag
    • Y. Kuang and A. Feldstein (1990), 'Monotonic and oscillatory solutions of a linear neutral delay equation with infinite lag', SIAM J. Math. Anal. 21, 1633-1641.
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 1633-1641
    • Kuang, Y.1    Feldstein, A.2
  • 167
    • 84966253976 scopus 로고
    • A new collocation-type method for Hammerstein integral equations
    • S. Kumar and I. H. Sloan (1987), 'A new collocation-type method for Hammerstein integral equations', Math. Comp. 48, 585-593.
    • (1987) Math. Comp. , vol.48 , pp. 585-593
    • Kumar, S.1    Sloan, I.H.2
  • 170
    • 2942668522 scopus 로고
    • Thèse de doctorat, Gauthier-Villars, Paris; J. de Math
    • T. Lalesco (1908), Sur l'équation de Volterra, Thèse de doctorat, Gauthier-Villars, Paris; J. de Math.
    • (1908) Sur l'Équation de Volterra , vol.4 , pp. 125-202
    • Lalesco, T.1
  • 171
    • 2942653261 scopus 로고
    • Sur une équation intégrale du type Volterra
    • T. Lalesco (1911), 'Sur une équation intégrale du type Volterra', CR Acad. Sci. Paris 52, 579-580.
    • (1911) CR Acad. Sci. Paris , vol.52 , pp. 579-580
    • Lalesco, T.1
  • 173
  • 174
    • 2942679579 scopus 로고    scopus 로고
    • Asymptotic stability of numerical solution of pantograph delay differential equations
    • D.-S. Li and M.-Z. Liu (1999), 'Asymptotic stability of numerical solution of pantograph delay differential equations' (in Chinese), J. Harbin Inst. Tech. 31, 57-59.
    • (1999) J. Harbin Inst. Tech. , vol.31 , pp. 57-59
    • Li, D.-S.1    Liu, M.-Z.2
  • 175
    • 2942668523 scopus 로고    scopus 로고
    • Numerical stability of θ-methods for pantograph delay differential equations
    • J. Liang and M. Liu (1996), 'Numerical stability of θ-methods for pantograph delay differential equations' (in Chinese), J. Numer. Methods Comput. Appl. 12, 271-278.
    • (1996) J. Numer. Methods Comput. Appl. , vol.12 , pp. 271-278
    • Liang, J.1    Liu, M.2
  • 176
    • 2942642573 scopus 로고    scopus 로고
    • The stability of θ-methods for pantograph delay differential equations
    • J. Liang, S. Qiu and M. Liu (1996), 'The stability of θ-methods for pantograph delay differential equations', Numer. Math. (Engl. Ser.) 5, 80-85.
    • (1996) Numer. Math. (Engl. Ser.) , vol.5 , pp. 80-85
    • Liang, J.1    Qiu, S.2    Liu, M.3
  • 177
    • 2942670750 scopus 로고
    • Comparison theorems for difference-differential equations
    • Q. Lin (1963), 'Comparison theorems for difference-differential equations', Sci. Sinica 12, 449.
    • (1963) Sci. Sinica , vol.12 , pp. 449
    • Lin, Q.1
  • 178
    • 2942677322 scopus 로고    scopus 로고
    • On solutions of evolution equations with proportional time delay
    • W. J. Liu and J. C. Clements (2002), 'On solutions of evolution equations with proportional time delay', Int. J. Differ. Equ. Appl. 4, 229-254.
    • (2002) Int. J. Differ. Equ. Appl. , vol.4 , pp. 229-254
    • Liu, W.J.1    Clements, J.C.2
  • 179
    • 21844488753 scopus 로고
    • Stability analysis of θ-methods for neutral functional-differential equations
    • Y. Liu (1995a), 'Stability analysis of θ-methods for neutral functional-differential equations', Numer. Math. 70, 473-485.
    • (1995) Numer. Math. , vol.70 , pp. 473-485
    • Liu, Y.1
  • 180
    • 0039455300 scopus 로고
    • The linear q-difference equation
    • Y. Liu (1995b), 'The linear q-difference equation', Appl. Math. Lett. 8, 15-18.
    • (1995) Appl. Math. Lett. , vol.8 , pp. 15-18
    • Liu, Y.1
  • 181
    • 0030523604 scopus 로고    scopus 로고
    • Asymptotic behaviour of functional-differential equations with proportional time delays
    • Y. Liu (1996a), 'Asymptotic behaviour of functional-differential equations with proportional time delays', Europ. J. Appl. Math. 7, 11-30.
    • (1996) Europ. J. Appl. Math. , vol.7 , pp. 11-30
    • Liu, Y.1
  • 182
    • 0030194116 scopus 로고    scopus 로고
    • On θ-methods for delay differential equations with infinite lag
    • Y. Liu (1996b), 'On θ-methods for delay differential equations with infinite lag', J. Comput. Appl. Math. 71, 177-190.
    • (1996) J. Comput. Appl. Math. , vol.71 , pp. 177-190
    • Liu, Y.1
  • 183
    • 0031212297 scopus 로고    scopus 로고
    • Numerical investigation of the pantograph equation
    • Y. Liu (1997), 'Numerical investigation of the pantograph equation', Appl. Numer. Math. 24, 309-317.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 309-317
    • Liu, Y.1
  • 184
    • 0041625708 scopus 로고    scopus 로고
    • Numerical solution of implicit neutral functional differential equations
    • Y. Liu (1999a), 'Numerical solution of implicit neutral functional differential equations', SIAM J. Numer. Anal. 36, 516-528.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 516-528
    • Liu, Y.1
  • 185
    • 0000579152 scopus 로고    scopus 로고
    • Runge-Kutta-collocation methods for systems of functional-differential and functional equations
    • Y. Liu (1999b), 'Runge-Kutta-collocation methods for systems of functional-differential and functional equations', Adv. Comput. Math. 11, 315-329.
    • (1999) Adv. Comput. Math. , vol.11 , pp. 315-329
    • Liu, Y.1
  • 186
    • 0020607199 scopus 로고
    • A block-by-block method for the numerical solution of Volterra delay integro-differential equations
    • A. Makroglou (1983), 'A block-by-block method for the numerical solution of Volterra delay integro-differential equations', Computing 30, 49-62.
    • (1983) Computing , vol.30 , pp. 49-62
    • Makroglou, A.1
  • 188
    • 84971942321 scopus 로고
    • Numerical methods for differential-algebraic equations
    • Cambridge University Press
    • R. März (1992), 'Numerical methods for differential-algebraic equations', in Acta Numerica, Vol. 1, Cambridge University Press, pp. 141-198.
    • (1992) Acta Numerica , vol.1 , pp. 141-198
    • März, R.1
  • 189
    • 0036679944 scopus 로고    scopus 로고
    • Differential algebraic equations anew
    • R. März (2002a), 'Differential algebraic equations anew', Appl. Numer. Math. 42, 315-335.
    • (2002) Appl. Numer. Math. , vol.42 , pp. 315-335
    • März, R.1
  • 190
    • 25044442201 scopus 로고    scopus 로고
    • The index of linear differential-algebraic equations with properly stated leading terms
    • R. März (2002b), 'The index of linear differential-algebraic equations with properly stated leading terms', Resultate Math. 42, 308-338.
    • (2002) Resultate Math. , vol.42 , pp. 308-338
    • März, R.1
  • 191
    • 0033349104 scopus 로고    scopus 로고
    • Asymptotic stability in the numerical solution of linear pure delay differential equations as abstract Cauchy problems
    • S. Maset (1999). 'Asymptotic stability in the numerical solution of linear pure delay differential equations as abstract Cauchy problems', J. Comput. Appl. Math. 111, 163-172.
    • (1999) J. Comput. Appl. Math. , vol.111 , pp. 163-172
    • Maset, S.1
  • 192
    • 0242624847 scopus 로고    scopus 로고
    • Numerical solution of retarded functional differential equations as abstract Cauchy problems
    • S. Maset (2003), 'Numerical solution of retarded functional differential equations as abstract Cauchy problems', J. Comput. Appl. Math. 161, 259-282.
    • (2003) J. Comput. Appl. Math. , vol.161 , pp. 259-282
    • Maset, S.1
  • 194
    • 2942677323 scopus 로고
    • Eine spezielle integralgleichung erster art
    • Numerical Treatment of Differential Equations, Oberwolfach 1976, R. Bulirsch, R. D. Grigorieff and J. Schr̈der, eds, Springer, Berlin/Heidelberg
    • T. Meis (1976), 'Eine spezielle Integralgleichung erster Art', in Numerical Treatment of Differential Equations, Oberwolfach 1976 (R. Bulirsch, R. D. Grigorieff and J. Schr̈der, eds), Vol. 631 of Lecture Notes in Mathematics, Springer, Berlin/Heidelberg, pp. 107-120.
    • (1976) Lecture Notes in Mathematics , vol.631 , pp. 107-120
    • Meis, T.1
  • 197
    • 0003211660 scopus 로고
    • The Phragmén-Lindelöf principle and a class of functional differential equations
    • (L. Weiss, ed.). Academic Press, New York
    • G.R. Morris, A. Feldstein and E. W. Bowen (1972), 'The Phragmén-Lindelöf principle and a class of functional differential equations', in Ordinary Differential Equations, Washington, DC, 1971 (L. Weiss, ed.). Academic Press, New York, pp. 513-540.
    • (1972) Ordinary Differential Equations, Washington, DC, 1971 , pp. 513-540
    • Morris, G.R.1    Feldstein, A.2    Bowen, E.W.3
  • 198
    • 25044451889 scopus 로고
    • Die Methode der sukzessiven Approximationen für eine Integralgleichung vom Typ Volterra-Sobolev
    • V. Mureşan (1984), 'Die Methode der sukzessiven Approximationen für eine Integralgleichung vom Typ Volterra-Sobolev', Mathematica (Cluj) 26, 129-136.
    • (1984) Mathematica (Cluj) , vol.26 , pp. 129-136
    • Mureşan, V.1
  • 199
    • 25044475167 scopus 로고    scopus 로고
    • On a class of Volterra integral equations with deviating argument
    • V. Mureşan (1999), 'On a class of Volterra integral equations with deviating argument', Studia Univ. Babeş-Bolyai Math. XLIV, 47-54.
    • (1999) Studia Univ. Babeş-Bolyai Math. , vol.44 , pp. 47-54
    • Mureşan, V.1
  • 200
    • 0037336074 scopus 로고    scopus 로고
    • On the attainable order of collocation methods for pantograph integro-differential equations
    • Y. Muroya, E. Ishiwata and H. Brunner (2002). 'On the attainable order of collocation methods for pantograph integro-differential equations', J. Comput. Appl. Math. 152, 347-366.
    • (2002) J. Comput. Appl. Math. , vol.152 , pp. 347-366
    • Muroya, Y.1    Ishiwata, E.2    Brunner, H.3
  • 202
    • 0008815916 scopus 로고
    • Characterization of jump discontinuities for state dependent delay differential equations
    • K. W. Neves and A. Feldstein (1976), 'Characterization of jump discontinuities for state dependent delay differential equations', J. Math. Anal. Appl. 56, 689-707.
    • (1976) J. Math. Anal. Appl , vol.56 , pp. 689-707
    • Neves, K.W.1    Feldstein, A.2
  • 203
    • 38249015876 scopus 로고
    • Software for the numerical solution of systems of functional differential equations with state-dependent delays
    • K. W. Neves and S. Thompson (1992), 'Software for the numerical solution of systems of functional differential equations with state-dependent delays', Appl. Numer. Math. 9, 385-401.
    • (1992) Appl. Numer. Math. , vol.9 , pp. 385-401
    • Neves, K.W.1    Thompson, S.2
  • 204
    • 0000810581 scopus 로고
    • Numerical treatment of delay differential equations by Hermite interpolation
    • H. J. Oberle and H. J. Pesch (1981), 'Numerical treatment of delay differential equations by Hermite interpolation', Numer. Math. 37, 235-255.
    • (1981) Numer. Math. , vol.37 , pp. 235-255
    • Oberle, H.J.1    Pesch, H.J.2
  • 205
    • 0001579514 scopus 로고
    • The dynamics of a current collection system for an electric locomotive
    • J. R. Ockendon and A. B. Tayler (1971), 'The dynamics of a current collection system for an electric locomotive', Proc. Roy. Soc. London Ser. A 322, 447-468.
    • (1971) Proc. Roy. Soc. London Ser. A , vol.322 , pp. 447-468
    • Ockendon, J.R.1    Tayler, A.B.2
  • 206
    • 0030556099 scopus 로고    scopus 로고
    • Characterization of the membrane theory of a clamped shell: The hyperbolic case
    • J. Piila (1996), 'Characterization of the membrane theory of a clamped shell: The hyperbolic case', Math. Methods Appl. Sci. 6, 169-194.
    • (1996) Math. Methods Appl. Sci. , vol.6 , pp. 169-194
    • Piila, J.1
  • 208
    • 2942675152 scopus 로고
    • A functional equation with contracting argument
    • T. P. Pukhnacheva (1990), 'A functional equation with contracting argument', Siberian Math. J. 31, 365-367.
    • (1990) Siberian Math. J , vol.31 , pp. 365-367
    • Pukhnacheva, T.P.1
  • 210
    • 2942675151 scopus 로고
    • Sur la B-stabilité pour une équation différentielle à retard
    • J. Reverdy (1990), 'Sur la B-stabilité pour une équation différentielle à retard'. CR Acad. Sci. Paris Sér. I Math. 310, 461-463.
    • (1990) CR Acad. Sci. Paris Sér. I Math. , vol.310 , pp. 461-463
    • Reverdy, J.1
  • 211
    • 0030589755 scopus 로고    scopus 로고
    • Bifurcation analysis of a chemostat model with a distributed delay
    • S. Ruan and G. S. K. Wolkowicz (1996), 'Bifurcation analysis of a chemostat model with a distributed delay', J. Math. Anal. Appl. 204, 786-812.
    • (1996) J. Math. Anal. Appl , vol.204 , pp. 786-812
    • Ruan, S.1    Wolkowicz, G.S.K.2
  • 213
    • 0001289473 scopus 로고
    • Reaction-diffusion equations with infinite delay
    • S. Ruan and J. Wu (1994), 'Reaction-diffusion equations with infinite delay', Canad. Appl. Math. Quart. 2, 485-550.
    • (1994) Canad. Appl. Math. Quart. , vol.2 , pp. 485-550
    • Ruan, S.1    Wu, J.2
  • 215
    • 84967460698 scopus 로고    scopus 로고
    • Analytic solutions of a nonlinear functional differential equation with proportional delays
    • J.-G. Si (2000), 'Analytic solutions of a nonlinear functional differential equation with proportional delays', Demonstratio Math. 33, 747-752.
    • (2000) Demonstratio Math. , vol.33 , pp. 747-752
    • Si, J.-G.1
  • 216
    • 2942668524 scopus 로고    scopus 로고
    • Analytic solutions of a functional differential equation with proportional delays
    • J.-G. Si and S. S. Cheng (2002), 'Analytic solutions of a functional differential equation with proportional delays', Bull. Korean Math. Soc. 39, 225-236.
    • (2002) Bull. Korean Math. Soc. , vol.39 , pp. 225-236
    • Si, J.-G.1    Cheng, S.S.2
  • 217
    • 0017328061 scopus 로고
    • On periodic solutions of a delay integral equation modelling epidemics
    • H. L. Smith (1977), 'On periodic solutions of a delay integral equation modelling epidemics', J. Math. Biol. 4, 69-80.
    • (1977) J. Math. Biol. , vol.4 , pp. 69-80
    • Smith, H.L.1
  • 218
    • 0031210214 scopus 로고    scopus 로고
    • Numerical stability, resolvent conditions and delay differential equations
    • M. N. Spijker (1997), 'Numerical stability, resolvent conditions and delay differential equations', Appl. Numer. Math. 24, 233-246.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 233-246
    • Spijker, M.N.1
  • 219
    • 0004905542 scopus 로고
    • Extended initial and forcing function semigroups generated by a functional equation
    • O. J. Staffans (1985a), 'Extended initial and forcing function semigroups generated by a functional equation', SIAM J. Math. Anal 16, 1034-1048.
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 1034-1048
    • Staffans, O.J.1
  • 220
    • 0039433320 scopus 로고
    • Some well-posed functional equations which generate semigroups
    • O. J. Staffans (1985b), 'Some well-posed functional equations which generate semigroups', J. Differential Equations 58, 157-191.
    • (1985) J. Differential Equations , vol.58 , pp. 157-191
    • Staffans, O.J.1
  • 221
    • 0000361452 scopus 로고    scopus 로고
    • On the attainable order of collocation methods for the delay differential equations with proportional delay
    • N. Takama, Y. Muroya and E. Ishiwata (2000), 'On the attainable order of collocation methods for the delay differential equations with proportional delay', BIT 40, 374-394.
    • (2000) BIT , vol.40 , pp. 374-394
    • Takama, N.1    Muroya, Y.2    Ishiwata, E.3
  • 222
    • 0015206438 scopus 로고
    • One-step methods for the numerical solution of Volterra functional differential equations
    • L. Tavernini (1971), 'One-step methods for the numerical solution of Volterra functional differential equations', SIAM J. Numer. Anal. 8, 786-795.
    • (1971) SIAM J. Numer. Anal. , vol.8 , pp. 786-795
    • Tavernini, L.1
  • 223
    • 0015758180 scopus 로고
    • Linear multistep methods for the numerical solution of Volterra functional differential equations
    • L. Tavernini (1973), 'Linear multistep methods for the numerical solution of Volterra functional differential equations', Appl. Anal. 3, 169-185.
    • (1973) Appl. Anal. , vol.3 , pp. 169-185
    • Tavernini, L.1
  • 224
    • 0040944200 scopus 로고
    • The approximate solution of Volterra differential systems with state dependent time lags
    • L. Tavernini (1978), 'The approximate solution of Volterra differential systems with state dependent time lags', SIAM J. Numer. Anal. 15, 1039-1052.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 1039-1052
    • Tavernini, L.1
  • 226
    • 2942638174 scopus 로고
    • Representation of the solutions to linear pantograph equations
    • J. Terjéki (1995), 'Representation of the solutions to linear pantograph equations', Acta Sci. Math. (Szeged) 60, 705-713.
    • (1995) Acta Sci. Math. (Szeged) , vol.60 , pp. 705-713
    • Terjéki, J.1
  • 227
    • 0345116416 scopus 로고    scopus 로고
    • Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models
    • H. R. Thieme and X.-Q. Zhao (2003), 'Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models', J. Differential Equations 195, 430-470.
    • (2003) J. Differential Equations , vol.195 , pp. 430-470
    • Thieme, H.R.1    Zhao, X.-Q.2
  • 228
    • 2942651023 scopus 로고
    • On some functional differential equations: Existence of solutions and difference approximations
    • R. J. Thompson (1968), 'On some functional differential equations: existence of solutions and difference approximations', SIAM J. Numer. Anal. 5, 475-487.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 475-487
    • Thompson, R.J.1
  • 229
    • 0029296752 scopus 로고
    • Numerical stability analysis of numerical methods for Volterra integral equations with delay argument
    • H.-J. Tian and J.-X. Kuang (1995), 'Numerical stability analysis of numerical methods for Volterra integral equations with delay argument', Appl. Math. Mech. (Engl. Edn) 16, 485-491.
    • (1995) Appl. Math. Mech. (Engl. Edn) , vol.16 , pp. 485-491
    • Tian, H.-J.1    Kuang, J.-X.2
  • 230
    • 38249024166 scopus 로고
    • Stability of numerical methods for delay differential equations
    • L. Torelli (1989), 'Stability of numerical methods for delay differential equations', J. Comput. Appl. Math. 25, 15-26.
    • (1989) J. Comput. Appl. Math. , vol.25 , pp. 15-26
    • Torelli, L.1
  • 231
    • 2942666323 scopus 로고    scopus 로고
    • A numerical approach for implicit non-linear neutral delay differential equations and its stability analysis
    • L. Torelli and R. Vermiglio (2003), 'A numerical approach for implicit non-linear neutral delay differential equations and its stability analysis', BIT 43, 195-215.
    • (2003) BIT , vol.43 , pp. 195-215
    • Torelli, L.1    Vermiglio, R.2
  • 232
    • 2942694423 scopus 로고
    • A neutral functional differential equation with an unbounded kernel
    • J. Turi and W. Desch (1993), 'A neutral functional differential equation with an unbounded kernel', J. Integral Equations Appl. 5, 569-582.
    • (1993) J. Integral Equations Appl. , vol.5 , pp. 569-582
    • Turi, J.1    Desch, W.2
  • 233
    • 2942670751 scopus 로고
    • Sur les équations fonctionnelles de Volterra et leurs applications à certains problémes de la physique mathématique
    • A. Tychonoff (1938), 'Sur les équations fonctionnelles de Volterra et leurs applications à certains problémes de la physique mathématique', Bull Univ. d'État de Moscou Sér. Internat. Sér. A Math. Méchan. 1, 1-25.
    • (1938) Bull Univ. d'État de Moscou Sér. Internat. Sér. A Math. Méchan. , vol.1 , pp. 1-25
    • Tychonoff, A.1
  • 234
    • 25044446071 scopus 로고
    • Convergence theorems of some numerical approximation scheme for the class of nonlinear integral equation
    • P. Vâţǎ (1978), 'Convergence theorems of some numerical approximation scheme for the class of nonlinear integral equation', Bul. Univ. Galaţi Fasc. II Mat. Fiz. Mec. Teoret. 1, 25-33.
    • (1978) Bul. Univ. Galaţi Fasc. II Mat. Fiz. Mec. Teoret. , vol.1 , pp. 25-33
    • Vâţǎ, P.1
  • 235
    • 51249177238 scopus 로고
    • A one-step subregion method for delay differential equations
    • R. Vermiglio (1985), 'A one-step subregion method for delay differential equations', Calcolo 22, 429-455.
    • (1985) Calcolo , vol.22 , pp. 429-455
    • Vermiglio, R.1
  • 236
    • 0040133311 scopus 로고
    • Natural continuous extension of Runge-kutta methods for volterra integrodifferential equations
    • R. Vermiglio (1988), 'Natural continuous extension of Runge-Kutta methods for Volterra integrodifferential equations', Numer. Math. 53, 439-458.
    • (1988) Numer. Math. , vol.53 , pp. 439-458
    • Vermiglio, R.1
  • 237
    • 0001397336 scopus 로고
    • On the stability of Runge-Kutta methods for delay integral equations
    • R. Vermiglio (1992), 'On the stability of Runge-Kutta methods for delay integral equations', Numer. Math. 81, 561-577.
    • (1992) Numer. Math. , vol.81 , pp. 561-577
    • Vermiglio, R.1
  • 238
    • 2942666323 scopus 로고    scopus 로고
    • A stable numerical approach for implicit non-linear neutral delay differential equations
    • R. Vermiglio and L. Torelli (1998), 'A stable numerical approach for implicit non-linear neutral delay differential equations', BIT 43, 195-215.
    • (1998) BIT , vol.43 , pp. 195-215
    • Vermiglio, R.1    Torelli, L.2
  • 239
    • 38249002225 scopus 로고
    • Multistep natural continuous extensions of Runge-kutta methods: The potential for stable interpolation
    • R. Vermiglio and M. Zennaro (1993), 'Multistep natural continuous extensions of Runge-Kutta methods: The potential for stable interpolation', Appl. Numer. Math. 12, 521-546.
    • (1993) Appl. Numer. Math. , vol.12 , pp. 521-546
    • Vermiglio, R.1    Zennaro, M.2
  • 241
    • 0038950463 scopus 로고
    • Sulla inversione degli integrali definiti
    • (Nota I); 400-408 (Nota II); 557-567 (Nota III): 693-708 (Nota IV)
    • V. Volterra (1896), 'Sulla inversione degli integrali definiti', Atti R. Accad. Sci. Torino 31, 311-323 (Nota I); 400-408 (Nota II); 557-567 (Nota III): 693-708 (Nota IV).
    • (1896) Atti R. Accad. Sci. Torino , vol.31 , pp. 311-323
    • Volterra, V.1
  • 242
    • 51249193083 scopus 로고
    • Sopra alcune questioni di inversione di integrali definite
    • V. Volterra (1897), 'Sopra alcune questioni di inversione di integrali definite', Ann. Mat. Pura Appl. 25, 139-178.
    • (1897) Ann. Mat. Pura Appl. , vol.25 , pp. 139-178
    • Volterra, V.1
  • 243
    • 2942679578 scopus 로고
    • Sulle equazioni integro-differenziali
    • V. Volterra (1909), 'Sulle equazioni integro-differenziali, Rend. R. Accad. Lincei, 18, 167-174.
    • (1909) Rend. R. Accad. Lincei , vol.18 , pp. 167-174
    • Volterra, V.1
  • 244
    • 2442676426 scopus 로고
    • Sur les équations intégro-différentielles et leurs applications
    • V. Volterra (1912), 'Sur les équations intégro-différentielles et leurs applications', Acta Math. 35, 295-356.
    • (1912) Acta Math. , vol.35 , pp. 295-356
    • Volterra, V.1
  • 246
    • 0002924819 scopus 로고
    • Variazioni e fluttuazioni del numero d'individui in specie animali conviventi
    • V. Volterra (1927), 'Variazioni e fluttuazioni del numero d'individui in specie animali conviventi', Memorie del R. Comitato talassografico italiano CXXXI; also Volterra (1956), Vol. V, 1-111.
    • (1927) Memorie del R. Comitato Talassografico Italiano , vol.131
    • Volterra, V.1
  • 247
    • 2942694425 scopus 로고
    • V. Volterra (1927), 'Variazioni e fluttuazioni del numero d'individui in specie animali conviventi', Memorie del R. Comitato talassografico italiano CXXXI; also Volterra (1956), Vol. V, 1-111.
    • (1956) Memorie del R. Comitato Talassografico Italiano , vol.5 , pp. 1-111
    • Volterra1
  • 248
    • 0000767629 scopus 로고
    • Sur la théorie mathématique des phénomèmes héréditaires
    • V. Volterra (1928), 'Sur la théorie mathématique des phénomèmes héréditaires', J. Math. Pures Appl. 7, 249-298.
    • (1928) J. Math. Pures Appl. , vol.7 , pp. 249-298
    • Volterra, V.1
  • 250
    • 0038432007 scopus 로고
    • Remarques sur la Note de M. Régniergnier et Mlle Lambin
    • V. Volterra (1934), 'Remarques sur la Note de M. Régnier et Mlle Lambin', CR Acad. Sci. 199, 1684-1686; also: Volterra (1956), Vol. V, 390-391.
    • (1934) CR Acad. Sci. , vol.199 , pp. 1684-1686
    • Volterra, V.1
  • 251
    • 2942666325 scopus 로고
    • V. Volterra (1934), 'Remarques sur la Note de M. Régnier et Mlle Lambin', CR Acad. Sci. 199, 1684-1686; also: Volterra (1956), Vol. V, 390-391.
    • (1956) CR Acad. Sci. , vol.5 , pp. 390-391
    • Volterra1
  • 252
    • 2942640339 scopus 로고
    • The general equations of biological strife in the case of historical actions
    • V. Volterra (1939). 'The general equations of biological strife in the case of historical actions', Proc. Edinburgh Math. Soc. 6, 4-10.
    • (1939) Proc. Edinburgh Math. Soc. , vol.6 , pp. 4-10
    • Volterra, V.1
  • 253
    • 25044464259 scopus 로고
    • (1956-1962), Accademia Nazionale dei Lincei, Roma
    • V. Volterra (1956), Opere Matematiche, Vol. I-V (1956-1962), Accademia Nazionale dei Lincei, Roma.
    • (1956) Opere Matematiche , vol.1-5
    • Volterra, V.1
  • 258
    • 0001302842 scopus 로고
    • The tracking of derivative discontinuities in systems of delay differential equations
    • D. R. Willé and C. T. H. Baker (1992), The tracking of derivative discontinuities in systems of delay differential equations', Appl. Numer. Math. 9, 209-222.
    • (1992) Appl. Numer. Math. , vol.9 , pp. 209-222
    • Willé, D.R.1    Baker, C.T.H.2
  • 259
    • 2942679577 scopus 로고
    • Numerische Lösung Volterrascher Integralgleichungen zweiter Art mit Nacheilung unter Verwendung kubischer Splines
    • J. Wolff (1982), 'Numerische Lösung Volterrascher Integralgleichungen zweiter Art mit Nacheilung unter Verwendung kubischer Splines', Wiss. Z. Pädag. Hochschule 'Liselotte Herrmann' Güstrow Math. Nat.-Wiss. Fak. 20, 225-244.
    • (1982) Wiss. Z. Pädag. Hochschule 'Liselotte Herrmann' Güstrow Math. Nat.-Wiss. Fak. , vol.20 , pp. 225-244
    • Wolff, J.1
  • 261
    • 2942672929 scopus 로고
    • Volterra integral equations with unknown delay time
    • Y. Yatsenko (1995), 'Volterra integral equations with unknown delay time', Methods Appl. Anal. 2, 408-419.
    • (1995) Methods Appl. Anal. , vol.2 , pp. 408-419
    • Yatsenko, Y.1
  • 263
    • 84966233444 scopus 로고
    • Natural continuous extensions of Runge-Kutta methods
    • M. Zennaro (1986), 'Natural continuous extensions of Runge-Kutta methods', Math. Comp. 46, 119-133.
    • (1986) Math. Comp. , vol.46 , pp. 119-133
    • Zennaro, M.1
  • 264
    • 38249006326 scopus 로고
    • Contractivity of Runge-Kutta methods with respect to forcing terms
    • M. Zennaro (1993), 'Contractivity of Runge-Kutta methods with respect to forcing terms', Appl. Numer. Math. 10, 321-345.
    • (1993) Appl. Numer. Math. , vol.10 , pp. 321-345
    • Zennaro, M.1
  • 265
    • 0000446512 scopus 로고
    • Delay differential equations: Theory and numerics
    • Theory and Numerics of Ordinary and Partial Differential Equations, Leicester 1994 (M. Ainsworth et al., eds), Clarendon Press, Oxford
    • M. Zennaro (1995), 'Delay differential equations: Theory and numerics', in Theory and Numerics of Ordinary and Partial Differential Equations, Leicester 1994 (M. Ainsworth et al., eds), Vol. 4 of Advances in Numerical Analysis, Clarendon Press, Oxford, pp. 291-333.
    • (1995) Advances in Numerical Analysis , vol.4 , pp. 291-333
    • Zennaro, M.1
  • 266
    • 0031501318 scopus 로고    scopus 로고
    • Asymptotic stability analysis of Runge-kutta methods for nonlinear systems of delay differential equations
    • M. Zennaro (1997), 'Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations', Numer. Math. 77, 549-563.
    • (1997) Numer. Math. , vol.77 , pp. 549-563
    • Zennaro, M.1
  • 267
    • 2942653262 scopus 로고    scopus 로고
    • Stability analysis of Runge-kutta methods for nonlinear Volterra delay-integro-differential equations
    • to appear
    • C. Zhang and S. Vandewalle (2004), 'Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations', IMA J. Numer. Anal., to appear.
    • (2004) IMA J. Numer. Anal.
    • Zhang, C.1    Vandewalle, S.2
  • 268
    • 0036141582 scopus 로고    scopus 로고
    • Stability of BDF methods for nonlinear Volterra integral equations with delay
    • C. J. Zhang and X. X. Liao (2002), 'Stability of BDF methods for nonlinear Volterra integral equations with delay', Comput. Math. Appl. 43, 95-102.
    • (2002) Comput. Math. Appl. , vol.43 , pp. 95-102
    • Zhang, C.J.1    Liao, X.X.2
  • 269
  • 270
    • 2942672930 scopus 로고    scopus 로고
    • Collocation approximations for second-order differential equations and Volterra integro-differential equations with variable delays
    • W. Zhang and H. Brunner (1998), 'Collocation approximations for second-order differential equations and Volterra integro-differential equations with variable delays', Canad. Appl. Math. Quart. 6, 269-285.
    • (1998) Canad. Appl. Math. Quart. , vol.6 , pp. 269-285
    • Zhang, W.1    Brunner, H.2
  • 272
    • 0242401393 scopus 로고    scopus 로고
    • Stability in the numerical solution of linear parabolic equations with a delay term
    • B. Zubik-Kowal (1999), 'Stability in the numerical solution of linear parabolic equations with a delay term', BIT 41, 191-206.
    • (1999) BIT , vol.41 , pp. 191-206
    • Zubik-Kowal, B.1
  • 273
    • 0033293668 scopus 로고    scopus 로고
    • Waveform relaxation for functional-differential equations
    • B. Zubik-Kowal and S. Vandewalle (1999), 'Waveform relaxation for functional-differential equations', SIAM J. Sci. Comput. 21, 207-226.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 207-226
    • Zubik-Kowal, B.1    Vandewalle, S.2


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