Impulsive continuous Runge–Kutta methods for impulsive delay differential equations

Abstract

The classical continuous Runge–Kutta methods are widely applied to compute the numerical solutions of delay differential equations without impulsive perturbations. However, the classical continuous Runge–Kutta methods cannot be applied directly to impulsive delay differential equations, because the exact solutions of the impulsive delay differential equations are not continuous. In this paper, impulsive continuous Runge–Kutta methods are constructed for impulsive delay differential equations with the variable delay based on the theory of continuous Runge–Kutta methods, convergence of the constructed numerical methods is studied and some numerical examples are given to confirm the theoretical results.