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

Year 2022, Volume: 5 Issue: 3, 107 - 116, 30.09.2022

Hefan Yin Qi Wang

https://doi.org/10.32323/ujma.1105072

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

Supporting Institution

Natural Science Foundation of Guangdong Province

Project Number

2017A030313031

Thanks

This study is supported by the Natural Science Foundation of Guangdong Province with the project number 2017A030313031.

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