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

X. Liu, M. Z. Liu

• 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.