Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system

Applied Mathematics and Computation

Volumn 167, Issue 2, 2005, Pages 1062-1079

  Zhao, J J ^a   Xu, Y ^a   Liu, M Z ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Delay integro differential equations; Numerical methods; Stability

Indexed keywords

LINEAR SYSTEMS; NUMERICAL METHODS; STABILITY;

DELAY-INTEGRO-DIFFERENTIAL SYSTEM; STABILITY ANALYSIS;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 25144525618     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.08.003     Document Type: Article

References (24)

1. L.V. Ahlfors Complex Analysis 2004 McGraw-Hill Beijing
2. H. Ardt, and C.T.H. Baker Runge-Kutta Formulae Applied to Volterra Functional Equations with a Fixed Delay 1988 Teubner Leipzig
3. C.T.H. Baker, and N.J. Frod Stability properties of a scheme for the approximate solution of a delay-integro-differential equation Appl. Numer. Math. 9 1992 357 370
4. C.T.H. Baker, and A. Tang Stability analysis of continuous implicit Runge-Kutta methods for Volterra integro-differential systems with unbounded delays Appl. Numer. Math. 24 1997 153 173
5. A. Bellen, and M. Zennaro Numerical Methods for Delay Differential Equations 2003 Oxford University Press New York
6. G.A. Bocharov, and F.A. Rihan Numerical modelling in biosciences with delay differential equations J. Comput. Appl. Math. 125 2000 183 199
7. R.K. Brayton, and R.A. Willoughby On the numerical integration of a symmetric system of difference-differential equations of neutral type J. Math. Anal. Appl. 18 1967 182 189
8. K.E. Brenan, S.L. Campbell, and L.R. Petzold Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations second ed. 1995 SIAM Philadelphia, PA
9. H. Brunner, The numerical solutions of neutral Volterra integro-differential equations with delay arguments, in: Proceedings SCADE'93, Auckland, 1993.
10. W.H. Enright, and M. Hu Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay Appl. Numer. Math. 24 1997 175 190
11. E. Hairer, and G. Wanner Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems 1991 Springer-Verlag Berlin
12. J.K. Hale, and S.M. Verduyn Lunel Introduction to Functional Differential Equations 1993 Springer-Verlag New York
13. K.J. in't Hout, Stability analysis of Runge-Kutta methods for system of delay differential equations, Report TW-95-08, Leiden University, Netherlands, 1995.
14. Z. Jackiewicz Quasilinear multistep methods and variable-step predictor-corrector methods for neutral functional-differential equations SIAM J. Numer. Anal. 23 1986 423 452
15. A. Jerri Introduction to Integral Equations with Applications 1999 Wiley New York
16. T. Koto Stability of Runge-Kutta methods for delay integro-differential equations J. Comput. Appl. Math. 145 2002 483 492
17. T. Koto Stability of θ-methods for delay integro-differential equations J. Comput. Appl. Math. 161 2003 393 404
18. J.X. Kuang, J.X. Xiang, and H.J. Tian The asymptotic stability of one-parameter methods for neutral differential equations BIT 34 1994 400 408
19. M.Z. Liu, and M.N. Spijker The stability of θ-method in the numerical solution of delay differential equations IMA J. Numer. Anal. 10 1990 31 48
20. L.R. Petzold, Numerical Solution of Differential-Algebraic Equations, Advances in Numerical Analysis VI, Springer, New York, 1995.
21. C.J. Zhang, and X.X. Liao Stability of BDF methods for nonlinear Volterra integral equations with delay Comput. Math. Appl. 43 2002 95 102
22. C.J. Zhang, and S. Vandewalle Stability analysis of Volterra delay-integro-differential equations and their backward differentiation time discretization J. Comput. Appl. Math. 164-165 2004 797 814
23. C.J. Zhang, and S. Vandewalle Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-differential equations IMA J. Numer. Anal. 24 2004 193 214
24. W.J. Zhu, and L.R. Petzold Asymptotic stability of linear delay differential-algebraic equations and numerical methods Appl. Numer. Math. 24 1997 247 264