Oscillation of Runge-Kutta methods for advanced impulsive differential equations with piecewise constant arguments

Advances in Difference Equations

Gui-Lai Zhang¹ 

[1] School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, China

关键词: impulsive differential equations;    piecewise constant arguments;    Runge-Kutta methods;    oscillation;    Padé approximation;   

DOI  :  10.1186/s13662-016-1067-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to study oscillation of Runge-Kutta methods for linear advanced impulsive differential equations with piecewise constant arguments. We obtain conditions of oscillation and nonoscillation for Runge-Kutta methods. Moreover, we prove that the oscillation of the exact solution is preserved by the θ-methods. It turns out that the zeros of the piecewise linear interpolation functions of the numerical solution converge to the zeros of the exact solution. We give some numerical examples to confirm the theoretical results.

【 授权许可】

CC BY