Numerical Stability of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments with Matrix Coefficients

Abstract

The paper discusses the analytical stability and numerical stability of differential equations with piecewise constant arguments with matrix coefficients. It is proved that the Runge-Kutta method can keep the convergence order. The recurrence relation of the Runge-Kutta method applied to the equations is obtained. Then, the stability conditions of the numerical solution under different matrix coefficients are given by Pade approximation and order star theory. Finally, the conclusions are verified by several numerical experiments.