Stability of continuous Runge-Kutta-type methods for nonlinear neutral delay-differential equations

摘要

This paper provides results on the correct simulation, when using continuous Runge-Kutta methods, of certain stability properties of nonlinear neutral delay-differential equations (NDDEs) y'(t) =f(t,y{t),y(t- τ{t)),y'(t - τ(t)))(t ≥ t_0). In particular, it is shown that certain continuous Runge-Kutta methods based upon the backward Euler method or the 2-stage Lobatto IIIC method, combined with linear interpolation, are CRN-stable and asymptotically stable for NDDEs.