Nonlinear Stability of Natural Runge-Kutta Methods for Neutral Delay Differential Equations

Abstract

This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonliner NDDEs, are given. In particular, it is shown thar the ($k,l$)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.