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.