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

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⩾t0). 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 GRN-stable and asymptotically stable for NDDEs.