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 discussed. It is shown that the method is convergent under the assumption that the splitting function satisfies only the one side Lipschitz condition with respect to some arguments and the Lipschitz condition with respect to the others. The conditions given in the paper also guarantee the existence and uniqueness of the solution to the initial problem discussed in the paper. The convergence of the perturbed continuous time waveform relaxation method is also discussed.