Stability of Runge-Kutta methods in the numerical solution of equation u′(t)=au(t)+a0u([t])

Journal of Computational and Applied Mathematics

Volumn 166, Issue 2, 2004, Pages 361-370

  Liu, M Z ^a   Song, M H ^a   Yang, Z W ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Asymptotic stability; Delay differential equation; Piecewise continuous arguments

Indexed keywords

COMPUTATIONAL METHODS; NUMERICAL METHODS;

NUMERICAL SOLUTIONS; STABILITY REGIONS;

RUNGE KUTTA METHODS;

MATHEMATICAL ANALYSIS;

EID: 1542530071     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.04.002     Document Type: Article

References (13)

1. Busenberg S. Cooke K.L. Models of vertically transmitted diseases with sequential-continuous dynamics Lakshmikantham V. Nonlinear Phenomena in Mathematical Sciences 1982 179-187 Academic Press New York
2. Butcher J.C. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods 1987 Wiley New York
3. Cooke K.L. Wiener J. Retarded differential equations with piecewise constant delays J. Math. Anal. Appl. 99 1984 265-297
4. Dekker K. Verwer J.G. Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations 1984 North-Holland Amsterdam
5. Hairer E. Nørsett S.P. Wanner G. Solving Ordinary Differential Equations II, Stiff and Differential Algebraic Problems 1993 Springer New York
6. Iserles A. Nørsett S.P. Order stars and rational approximations to exp(z) Appl. Numer. Math. 5 1989 63-70
7. Kocic V.L. Ladas G. Global Behavior of Nonlinear Difference Equations of Higher Order with Applications 1993 Kluwer Academic Publishers Dordrecht
8. Liu Pingzhou Gopalsamy K. Global stability and chaos in a population model with piecewise constant arguments Appl. Math. Comput. 101 1999 63-88
9. Shah S.M. Wiener J. Advanced differential equations with piecewise constant argument deviations Internat. J. Math. Math. Sci. 6 1983 671-703
10. Wanner G. Hairer E. Nørsett S.P. Order stars and stability theorems BIT 18 1978 475-489
11. Wiener J. Differential equations with piecewise constant delays Lakshmikantham V. Trends in the Theory and Practice of Nonlinear Differential Equations 1983 547-552 Marcel Dekker New York
12. Wiener J. Pointwise initial-value problems for functional differential equations Knowles I.W. Lewis R.T. Differential Equations 1984 571-580 North-Holland New York
13. Wiener J. Generalized Solutions of Differential Equations 1993 World Scientific Singapore