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

Authors : Hefan YİN, Qi WANG

Pages : 107-116

Doi:10.32323/ujma.1105072

View : 17 | Download : 10

Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :The paper discusses the analytical stability and numerical stability of differential equations with piecewise constant arguments with matrix coefficients. Firstly, the Runge-Kutta method is applied to the equation and the recurrence relationship of the numerical solution of the equation is obtained. Secondly, it is proved that the Runge-Kutta method can preserve the convergence order. Thirdly, the stability conditions of the numerical solution under different matrix coefficients are given by Pad$\acute{e}$ approximation and order star theory. Finally, the conclusions are verified by several numerical experiments.
Keywords : Runge Kutta methods, analytical stability, numerical stability