Stability analysis of Runge-Kutta methods for nonlinear functional differential and functional equations

Abstract

This paper is concerned with the numerical stability of Runge-Kutta methods for a class of nonlinear functional differential and functional equations. The sufficient conditions for the stability and asymptotic stability of (k, l) -algebraically stable Runge-Kutta methods are derived. A numerical test is given to confirm the theoretical results. © 2014 Yuexin Yu et al.