Stability analysis of Runge–Kutta methods for differential equations with piecewise continuous arguments of mixed type

Abstract

This paper deals with the stability analysis of the Runge–Kutta methods for a differential equation with piecewise continuous arguments of mixed type. The stability regions of the analytical solution are given. The necessary and sufficient conditions under which the numerical solution is asymptotically stable are discussed. The conditions under which the analytical stability region is contained in the numerical stability region are obtained and some numerical experiments are given.

Keywords:

• differential equations
• piecewise continuous
• Runge–Kutta methods
• asymptotic stability
• Padé approximation

2000 AMS Subject Classifications :

• 65L20
• 65M12
• 65N12

Acknowledgements

This work is supported by National Natural Science Foundation of China (No. 10572154) and NCET-06-0731. The authors are very grateful to Prof. Mingzhu Liu for his detailed comments and helpful suggestions.