Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations

Abstract

Abstract In this paper, asymptotical stability of the exact solutions of nonlinear impulsive ordinary differential equations is studied under Lipschitz conditions. Under these conditions, asymptotical stability of Runge–Kutta methods is studied by the theory of Padé approximation. And two simple examples are given to illustrate the conclusions.

Keywords

• Impulsive differential equation
• Runge–Kutta method
• Lipschitz condition
• Asymptotical stability