Alternating splitting waveform relaxation method and its successive overrelaxation acceleration

For the large sparse implicit linear initial value problem, we present a block successive overrelaxation scheme for the alternating direction implicit waveform relaxation method to further accelerate its convergence speed, and discuss the convergence property of the resulting iteration method in detail. Numerical implementations about several non-Hermitian implicit linear initial value problems show that the alternating direction implicit waveform relaxation method is very effective, and the block successive overrelaxation technique really accelerates its convergence speed.