Waveform relaxation for functional-differential equations

The convergence of waveform relaxation techniques for solving functional-differential equations is studied. New error estimates are derived that hold under linear and nonlinear conditions for the right-hand side of the equation. Sharp error bounds are obtained under generalized time-dependent Lipschitz conditions. The convergence of the waveform method and the quality of the a priori error bounds are illustrated by means of extensive numerical data obtained by applying the method of lines to three partial functional-differential equations.