메뉴 건너뛰기




Volumn 43, Issue 5, 2005, Pages 1934-1949

Optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays

Author keywords

Collocation method; Delay integral equation; Iterated collocation solution; Optimal order of superconvergence; Proportional delays

Indexed keywords

APPROXIMATION THEORY; INTEGRAL EQUATIONS; ITERATIVE METHODS; POLYNOMIALS; PROBLEM SOLVING;

EID: 33646380053     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040615705     Document Type: Article
Times cited : (35)

References (25)
  • 1
    • 0007145654 scopus 로고
    • Sulle equazioni integrals
    • G. ANDREOLI, Sulle equazioni integrals, Rend. Cire. Mat. Palermo, 37 (1914), pp. 76-112.
    • (1914) Rend. Cire. Mat. Palermo , vol.37 , pp. 76-112
    • Andreoli, G.1
  • 2
    • 0021449148 scopus 로고
    • One-step collocation for delay differential equations
    • A. BELLEN, One-step collocation for delay differential equations, J. Comput. Appl. Math., 10 (1984), pp. 275-283.
    • (1984) J. Comput. Appl. Math. , vol.10 , pp. 275-283
    • Bellen, A.1
  • 3
    • 84968494814 scopus 로고
    • Iterated collocation methods for Volterra integral equations with delay arguments
    • H. BRUNNER, Iterated collocation methods for Volterra integral equations with delay arguments, Math. Comp., 62 (1994), pp. 581-599.
    • (1994) Math. Comp. , vol.62 , pp. 581-599
    • Brunner, H.1
  • 4
    • 0002039485 scopus 로고    scopus 로고
    • On the discretization of differential and Volterra integral equations with variable delay
    • H. BRUNNER, On the discretization of differential and Volterra integral equations with variable delay, BIT, 37 (1997), pp. 1-12.
    • (1997) BIT , vol.37 , pp. 1-12
    • Brunner, H.1
  • 6
    • 0003213842 scopus 로고
    • The numerical solution of volterra equations
    • North-Holland, Amsterdam
    • H. BRUNNER AND P. J. VAN DER HOUWEN, The Numerical Solution of Volterra Equations, CWI Monographs 3, North-Holland, Amsterdam, 1986.
    • (1986) CWI Monographs , vol.3
    • Brunner, H.1    Van Der Houwen, P.J.2
  • 7
    • 0035541115 scopus 로고    scopus 로고
    • Geometric meshes in collocation methods for Volterra integral equations with proportional delays
    • H. BRUNNER, Q. HU, AND Q. LIN, Geometric meshes in collocation methods for Volterra integral equations with proportional delays, IMA J. Numer. Anal., 21 (2001), pp. 783-798.
    • (2001) IMA J. Numer. Anal. , vol.21 , pp. 783-798
    • Brunner, H.1    Hu, Q.2    Lin, Q.3
  • 9
    • 0021214562 scopus 로고
    • Superconvergence results for the iterated projection method applied to a Fredholm integral equation of the second kind and the corresponding eigenvalue problem
    • F. CHATEHN AND R. LEBBAR, Superconvergence results for the iterated projection method applied to a Fredholm integral equation of the second kind and the corresponding eigenvalue problem, J. Integral Equations, 6 (1984), pp. 71-91.
    • (1984) J. Integral Equations , vol.6 , pp. 71-91
    • Chatehn, F.1    Lebbar, R.2
  • 10
    • 2942677317 scopus 로고    scopus 로고
    • Existence results and regularization techniques for severely ill-posed integrofunctional equations
    • A. M. DENISOV AND A. LORENZI, Existence results and regularization techniques for severely ill-posed integrofunctional equations, Boll. Un. Mat. Ital. B (7), 11 (1997), pp. 713-732.
    • (1997) Boll. Un. Mat. Ital. B (7) , vol.11 , pp. 713-732
    • Denisov, A.M.1    Lorenzi, A.2
  • 11
    • 2942672927 scopus 로고
    • Numerische behandlung einer volterraschen integralgleichung
    • R. ESSER, Numerische Behandlung einer Volterraschen Integralgleichung, Computing, 19 (1978), pp. 269-284.
    • (1978) Computing , vol.19 , pp. 269-284
    • Esser, R.1
  • 14
    • 0040714267 scopus 로고    scopus 로고
    • Interpolation correction for collocation solutions of Fredholm integro-differential equations
    • Q. HU, Interpolation correction for collocation solutions of Fredholm integro-differential equations, Math. Comp., 67 (1998), pp. 987-999.
    • (1998) Math. Comp. , vol.67 , pp. 987-999
    • Hu, Q.1
  • 15
    • 0033208056 scopus 로고    scopus 로고
    • Multilevel correction for discrete collocation solutions of Volterra integral equations with delay arguments
    • Q. HU, Multilevel correction for discrete collocation solutions of Volterra integral equations with delay arguments, Appl. Numer. Math., 31 (1999), pp. 159-171.
    • (1999) Appl. Numer. Math. , vol.31 , pp. 159-171
    • Hu, Q.1
  • 16
    • 0242709242 scopus 로고
    • Numerical analysis of delay differential equations with variable delays
    • A. ISERLES, Numerical analysis of delay differential equations with variable delays, Ann. Numer. Math., 1 (1994), pp. 133-152.
    • (1994) Ann. Numer. Math. , vol.1 , pp. 133-152
    • Iserles, A.1
  • 17
    • 84893735286 scopus 로고
    • On pantograph integro-differential equations
    • A. ISERLES AND Y. LIU, On pantograph integro-differential equations, J. Integral Equations Appl., 6 (1994), pp. 213-237.
    • (1994) J. Integral Equations Appl. , vol.6 , pp. 213-237
    • Iserles, A.1    Liu, Y.2
  • 18
    • 0003211660 scopus 로고
    • The Phragmén-Lindelöf principle and a class of functional differential equations
    • (Proc. Conf., Math. Res. Center, Naval Res. Lab., Washington, DC, 1971), L. Weise, ed., Academic Press, New York
    • G. R. MORRIS, A. FELDSTEIN, AND E. W. BOWEN, The Phragmén- Lindelöf principle and a class of functional differential equations, in Ordinary Differential Equations (Proc. Conf., Math. Res. Center, Naval Res. Lab., Washington, DC, 1971), L. Weise, ed., Academic Press, New York, 1972, pp. 513-540.
    • (1972) Ordinary Differential Equations , pp. 513-540
    • Morris, G.R.1    Feldstein, A.2    Bowen, E.W.3
  • 19
    • 25044475167 scopus 로고    scopus 로고
    • On a class of Volterra integral equations with deviating argument
    • V. MUREŞAN, On a class of Volterra integral equations with deviating argument, Studia Univ. Babeg-Bolyai Math., 44 (1999), pp. 47-54.
    • (1999) Studia Univ. Babeg-bolyai Math. , vol.44 , pp. 47-54
    • Mureşan, V.1
  • 20
    • 0037336074 scopus 로고    scopus 로고
    • On the attainable order of collocation methods for pantograph integro-differential equations
    • Y. MUROYA, E. ISHIWATA, AND H. BRUNNER, On the attainable order of collocation methods for pantograph integro-differential equations, J. Comput. Appl. Math., 152 (2003), pp. 347-366.
    • (2003) J. Comput. Appl. Math. , vol.152 , pp. 347-366
    • Muroya, Y.1    Ishiwata, E.2    Brunner, H.3
  • 21
    • 0030556099 scopus 로고    scopus 로고
    • Characterization of the membrane theory of a clamped shell. the hyperbolic case
    • J. PIILA, Characterization of the membrane theory of a clamped shell. The hyperbolic case, Math. Methods Appl. Sci., 6 (1996), pp. 169-194.
    • (1996) Math. Methods Appl. Sci. , vol.6 , pp. 169-194
    • Piila, J.1
  • 23
    • 0000361452 scopus 로고    scopus 로고
    • On the attainable order of collocation methods for delay differential equation with proportional delay
    • N. TAKAMA, Y. MUROYA, AND E. ISHIWATA, On the attainable order of collocation methods for delay differential equation with proportional delay, BIT, 40 (2000), pp. 374-394.
    • (2000) BIT , vol.40 , pp. 374-394
    • Takama, N.1    Muroya, Y.2    Ishiwata, E.3
  • 24
    • 51249193083 scopus 로고
    • Sopra alcune questioni di inversione di integrals definite
    • V. VOLTERRA, Sopra alcune questioni di inversione di integrals definite, Ann. Mat. Pura Appl. (2), 25 (1897), pp. 139-178.
    • (1897) Ann. Mat. Pura Appl. (2) , vol.25 , pp. 139-178
    • Volterra, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.