Error analysis of waveform relaxation method for semi-linear partial differential equations

The waveform relaxation (WR) method is investigated for semi-linear partial differential equations. Explicit error estimation is given for the iteration error. A way to combine WR with convergent numerical methods is proposed, the error of the combined method is analyzed and its convergence is proven. The effect of the application of time windows is discussed. Numerical tests are presented to confirm the theoretical results.