On the convergence of waveform relaxation methods for differential-functional systems of equations

In this paper the convergence of a waveform relaxation method applied to an initial value problem for the Volterra functional-differential system is d iscussed. It is shown that the method is convergent under the assumption th at the splitting function satisfies only the one side Lipschitz condition w ith respect to some arguments and the Lipschitz condition with respect to t he others. The conditions given in the paper also guarantee the existence a nd uniqueness of the solution to the initial problem discussed in the paper . The convergence of the perturbed continuous time waveform relaxation meth od is also discussed. (C) 1999 Academic Press.