Convergence of waveform relaxation methods for neutral delay differential equations

This paper gives sufficient conditions for existence and uniqueness of solutions and for the convergence of waveform relaxation methods for nonlinear neutral delay differential equations (NDDEs). By investigations into the continuous time iteration and the discrete time iteration processes that are obtained from algebraically stable and diagonally stable Runge–Kutta methods, it is shown that the method is convergent under the assumptions that the splitting function satisfies the one-sided Lipschitz condition with respect to some arguments and the Lipschitz condition with respect to the others.