Two Schemes of Impulsive Runge–Kutta Methods for Linear Differential Equations with Delayed Impulses

Abstract

In this paper, two different schemes of impulsive Runge–Kutta methods are constructed for a class of linear differential equations with delayed impulses. One scheme is convergent of order p if the corresponding Runge–Kutta method is p order. Another one in the general case is only convergent of order 1, but it is more concise and may suit for more complex differential equations with delayed impulses. Moreover, asymptotical stability conditions for the exact solution and numerical solutions are obtained, respectively. Finally, some numerical examples are provided to confirm the theoretical results.

Keywords

• impulsive Runge–Kutta methods
• impulsive <i>θ</i> methods
• convergence
• asymptotical stability