메뉴 건너뛰기




Volumn 343, Issue 2, 2008, Pages 724-732

Analytic solutions to a class of nonlinear infinite-delay-differential equations

Author keywords

Exact solution; Infinite delay differential equation; Reproducing kernel space

Indexed keywords


EID: 41949092838     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.01.101     Document Type: Article
Times cited : (23)

References (24)
  • 1
    • 0036031976 scopus 로고    scopus 로고
    • Preservation of superconvergence in the numerical integration of delay differential equations with proportional delay
    • Bellen A. Preservation of superconvergence in the numerical integration of delay differential equations with proportional delay. IMA J. Numer. Anal. 22 (2002) 529-536
    • (2002) IMA J. Numer. Anal. , vol.22 , pp. 529-536
    • Bellen, A.1
  • 2
    • 0035541115 scopus 로고    scopus 로고
    • Geometric meshes in collocation methods for Volterra integral equations with proportional delays
    • Brunner H., Hu Q., and Lin Q. Geometric meshes in collocation methods for Volterra integral equations with proportional delays. IMA J. Numer. Anal. 21 (2001) 783-798
    • (2001) IMA J. Numer. Anal. , vol.21 , pp. 783-798
    • Brunner, H.1    Hu, Q.2    Lin, Q.3
  • 3
    • 0000826399 scopus 로고    scopus 로고
    • On the attainable order of collocation methods for the neutral functional-differential equations with proportional delays
    • Ishiwata E. On the attainable order of collocation methods for the neutral functional-differential equations with proportional delays. Computing 64 (2000) 207-222
    • (2000) Computing , vol.64 , pp. 207-222
    • Ishiwata, E.1
  • 4
    • 0000361452 scopus 로고    scopus 로고
    • On the attainable order of collocation methods for the delay differential equations with proportional delay
    • Takama N., Muroya Y., and Ishiwata E. On the attainable order of collocation methods for the delay differential equations with proportional delay. BIT 40 (2000) 374-394
    • (2000) BIT , vol.40 , pp. 374-394
    • Takama, N.1    Muroya, Y.2    Ishiwata, E.3
  • 5
    • 34247183596 scopus 로고    scopus 로고
    • Rational approximation method for delay differential equations with proportional delay
    • Ishiwata E., and Muroya Y. Rational approximation method for delay differential equations with proportional delay. Appl. Math. Comput. 187 (2007) 741-747
    • (2007) Appl. Math. Comput. , vol.187 , pp. 741-747
    • Ishiwata, E.1    Muroya, Y.2
  • 6
    • 0037336074 scopus 로고    scopus 로고
    • On the attainable order of collocation methods for pantograph integro-differential equations
    • Muroya Y., Ishiwata E., and Brunner H. On the attainable order of collocation methods for pantograph integro-differential equations. J. Comput. Appl. Math. 152 (2003) 347-366
    • (2003) J. Comput. Appl. Math. , vol.152 , pp. 347-366
    • Muroya, Y.1    Ishiwata, E.2    Brunner, H.3
  • 7
    • 4644238532 scopus 로고
    • Functional differential equations: Some models and perturbation problems
    • Hale J.K., and Lasalle J.P. (Eds), Academic Press, New York
    • Cooke K.L. Functional differential equations: Some models and perturbation problems. In: Hale J.K., and Lasalle J.P. (Eds). Differential Equations and Dynamical Systems (1967), Academic Press, New York
    • (1967) Differential Equations and Dynamical Systems
    • Cooke, K.L.1
  • 8
    • 0002924799 scopus 로고
    • On certain type of functional differential equations
    • Feckan E. On certain type of functional differential equations. Math. Slovaca 43 (1993) 39-43
    • (1993) Math. Slovaca , vol.43 , pp. 39-43
    • Feckan, E.1
  • 9
    • 84968490632 scopus 로고
    • Existence and continuous dependence for a class of nonlinear neutral-differential equations
    • Grimm L.J. Existence and continuous dependence for a class of nonlinear neutral-differential equations. Proc. Amer. Math. Soc. 29 (1971) 467-473
    • (1971) Proc. Amer. Math. Soc. , vol.29 , pp. 467-473
    • Grimm, L.J.1
  • 10
    • 0000145833 scopus 로고
    • A two-body problem of classical electrodynamics: The one-dimensional case
    • Driver R.D. A two-body problem of classical electrodynamics: The one-dimensional case. Ann. Physics 21 (1963) 122-142
    • (1963) Ann. Physics , vol.21 , pp. 122-142
    • Driver, R.D.1
  • 11
    • 84968484393 scopus 로고
    • On the local existence of solutions of certain functional differential equations
    • Oberg R.J. On the local existence of solutions of certain functional differential equations. Proc. Amer. Math. Soc. 20 (1969) 295-302
    • (1969) Proc. Amer. Math. Soc. , vol.20 , pp. 295-302
    • Oberg, R.J.1
  • 12
    • 0007761940 scopus 로고
    • Existence and uniqueness of solutions of neutral delay-differential equations with state dependent delays
    • Jackiewicz Z. Existence and uniqueness of solutions of neutral delay-differential equations with state dependent delays. Funkcial. Ekvac. 30 (1987) 9-17
    • (1987) Funkcial. Ekvac. , vol.30 , pp. 9-17
    • Jackiewicz, Z.1
  • 13
    • 0036143146 scopus 로고    scopus 로고
    • Analytic solutions of a second-order iterative functional differential equation
    • Si J.-G., and Wang X.-P. Analytic solutions of a second-order iterative functional differential equation. Comput. Math. Appl. 43 (2002) 81-90
    • (2002) Comput. Math. Appl. , vol.43 , pp. 81-90
    • Si, J.-G.1    Wang, X.-P.2
  • 14
    • 33645638037 scopus 로고    scopus 로고
    • Spurious numerical solutions of delay differential equations
    • Tian H.-j., Fan L.-q., Zhang Y.-y., and Xiang J.-x. Spurious numerical solutions of delay differential equations. J. Comput. Math. 24 2 (2006) 181-192
    • (2006) J. Comput. Math. , vol.24 , Issue.2 , pp. 181-192
    • Tian, H.-j.1    Fan, L.-q.2    Zhang, Y.-y.3    Xiang, J.-x.4
  • 15
    • 30144436054 scopus 로고    scopus 로고
    • A class of two-step continuity Runge-Kutta methods for solving singular delay differential equations and its stability analysis
    • Leng X., Liu D.-g., Song X.-q., and Chen L.-r. A class of two-step continuity Runge-Kutta methods for solving singular delay differential equations and its stability analysis. J. Comput. Math. 23 6 (2005) 647-656
    • (2005) J. Comput. Math. , vol.23 , Issue.6 , pp. 647-656
    • Leng, X.1    Liu, D.-g.2    Song, X.-q.3    Chen, L.-r.4
  • 16
    • 0001060056 scopus 로고
    • Existence and uniqueness theorems for some functional differential equations of neutral type
    • Nussbaum R.D. Existence and uniqueness theorems for some functional differential equations of neutral type. J. Differential Equations 11 (1972) 607-623
    • (1972) J. Differential Equations , vol.11 , pp. 607-623
    • Nussbaum, R.D.1
  • 17
    • 0001255506 scopus 로고
    • Monotonic and oscillatory solutions of a linear neutral delay equation with infinite lag
    • Kuang Y., and Feldstein A. Monotonic and oscillatory solutions of a linear neutral delay equation with infinite lag. SIAM J. Math. Anal. 21 (1990) 1633-1641
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 1633-1641
    • Kuang, Y.1    Feldstein, A.2
  • 18
    • 0031081849 scopus 로고    scopus 로고
    • On neutral functional-differential equation with proportional delays
    • Iserles A., and Liu Y. On neutral functional-differential equation with proportional delays. J. Math. Anal. Appl. 207 (1997) 73-95
    • (1997) J. Math. Anal. Appl. , vol.207 , pp. 73-95
    • Iserles, A.1    Liu, Y.2
  • 19
    • 21844488753 scopus 로고
    • Stability analysis of θ-methods for neutral functional differential equations
    • Liu Y. Stability analysis of θ-methods for neutral functional differential equations. Numer. Math. 70 (1995) 473-485
    • (1995) Numer. Math. , vol.70 , pp. 473-485
    • Liu, Y.1
  • 20
    • 1942425045 scopus 로고    scopus 로고
    • Nonlinear stability of Runge-Kutta methods applied to infinite-delay-differential equations
    • Zhang C.J., and Sun G. Nonlinear stability of Runge-Kutta methods applied to infinite-delay-differential equations. Math. Comput. Modelling 39 (2004) 495-503
    • (2004) Math. Comput. Modelling , vol.39 , pp. 495-503
    • Zhang, C.J.1    Sun, G.2
  • 21
    • 0031276989 scopus 로고    scopus 로고
    • Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations
    • Zhang C.J., and Zhou S.Z. Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations. J. Comput. Appl. Math. 85 (1997) 225-237
    • (1997) J. Comput. Appl. Math. , vol.85 , pp. 225-237
    • Zhang, C.J.1    Zhou, S.Z.2
  • 22
    • 0033097062 scopus 로고    scopus 로고
    • Stability and error analysis of one-leg methods for nonlinear delay differential equations
    • Huang C.M., Li S.F., Fu H.Y., and Chen G.N. Stability and error analysis of one-leg methods for nonlinear delay differential equations. J. Comput. Appl. Math. 103 (1999) 263-279
    • (1999) J. Comput. Appl. Math. , vol.103 , pp. 263-279
    • Huang, C.M.1    Li, S.F.2    Fu, H.Y.3    Chen, G.N.4
  • 23
    • 31244435236 scopus 로고    scopus 로고
    • The discrete dynamics of nonlinear infinite-delay-differential equations
    • Zhang C.J., and Sun G. The discrete dynamics of nonlinear infinite-delay-differential equations. Appl. Math. Lett. 15 5 (2002) 521-526
    • (2002) Appl. Math. Lett. , vol.15 , Issue.5 , pp. 521-526
    • Zhang, C.J.1    Sun, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.