Stability and efficiency of waveform relaxation methods

We investigate the behaviour of Waveform Relaxation methods (WR) for some model problems. First, it is shown how convergence (of the iteration) is related to stability of some one-step integration schemes. Then, we investigate the computational complexity of a 1-D and 2-D heat equation when WR is used in combination with nested iteration and assess its efficiency, in particular, compared to straightforward methods based on Gaussian elimination. Finally, we present some results, showing the performance of WR