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 wave form 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. (C) 2008 Elsevier Ltd. All rights reserved.
convergence waveform relaxation methods nonlinear neutral delay differential equations continuous time iteration discrete time iteration runge-kutta methods