Asymptotic stability of Runge–Kutta methods for nonlinear differential equations with piecewise continuous arguments

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摘要

This paper deals with the asymptotic stability of numerical solutions for differential equations with piecewise continuous arguments (EPCAs). The necessary and sufficient condition is given for non-confluent Runge–Kutta methods to preserve the stability of nonlinear scalar EPCAs. As for systems, we prove that some algebraically stable methods can preserve the asymptotic stability.

论文关键词:Piecewise continuous arguments,Asymptotic stability,Runge–Kutta methods,Numerical solutions,Delay differential equations

论文评审过程:Received 25 December 2013, Revised 19 November 2014, Available online 8 December 2014.

论文官网地址:https://doi.org/10.1016/j.cam.2014.11.059