Stability analysis of Runge-Kutta methods for unbounded retarded differential equations with piecewise continuous arguments

Applied Mathematics and Computation

Volumn 191, Issue 1, 2007, Pages 57-66

  Liu, M Z ^a   Ma, S F ^a   Yang, Z W ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Asymptotic stability; Piecewise continuous arguments; The unbounded retarded differential equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; PIECEWISE LINEAR TECHNIQUES; STABILITY;

ASYMPTOTICAL STABILITY;

RUNGE KUTTA METHODS;

EID: 34547678229     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.12.008     Document Type: Article

References (13)

1. Butcher J.C. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods (1987), Wiley, New York
2. Cooke K.L., and Wiener J. Retarded differential equations with piecewise constant delays. J. Math. Anal. Appl. 99 (1984) 265-297
3. Dekker K., and Verwer J.G. Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations (1984), North-Holland, Amsterdam
4. Hairer E., Nørsett S.P., and Wanner G. Solving Ordinary Differential Equations II, Stiff and Differential Algebraic Problems (1993), Springer-Verlag, New York
5. Iserles A., and Nørsett S.P. Order stars and rational approximations to exp(z). Appl. Numer. Math. 5 (1989) 63-70
6. 0 u ([t]). J. Comput. Appl. Math. 166 (2004) 361-370
7. X.J. Ran, M.Z. Liu, Numerical methods for impulsive differential equation, Math. Comput. Model., submitted for publication.
8. Shah S.M., and Wiener J. Advanced differential equations with piecewise constant argument deviations. Int. J. Math. Sci. 6 (1983) 671-703
9. Song M.H., Yang Z.W., and Liu M.Z. Stability of θ-methods advanced differential equations with piecewise continuous argument. Comput. Math. Appl. 49 (2005) 1205-1301
10. Wanner G., Hairer E., and Nørsett S.P. Order stars and stability theorems. BIT 18 (1978)
11. Wiener J. Differential equations with piecewise constant delays. In: Lakshmikantham V. (Ed). Trends in the Theory and Practice of Nonlinear Differential Equations (1983), Marcel Dekker, New York 547-552
12. Wiener J. Generalised Solutions of Differential Equations (1993), World Scientific, Singapore
13. 1 u ([t - 1]). Appl. Math. Comput. 162 (2005) 37-50