Waveform relaxation for functional-differential equations

1The convergence of waveform relaxation techniques for solving functional-d ifferential equations is studied. New error estimates are derived that hold under linear and nonlinear conditions for the right-hand side of the equat ion. Sharp error bounds are obtained under generalized time-dependent Lipsc hitz conditions. The convergence of the waveform method and the quality of the a priori error bounds are illustrated by means of extensive numerical d ata obtained by applying the method of lines to three partial functional-di fferential equations.