SOR waveform relaxation methods for stochastic differential equations

Waveform relaxation for solving large-scale systems of ordinary differential equations has extended to stochastic differential equations (SDEs). This paper deals with the acceleration of the Gauss-Sediel waveform relaxation method for SDEs by successive overrelaxation (SOR) techniques. A sufficient condition of the linear convergence is obtained for the continuous time SOR waveform relaxation method. The discrete time SOR waveform relaxation method used in an actual implementation was also studied. We first prove that the general numerical schemes are convergent and then the particular method based on Euler scheme linearly converge to the Euler approximate solution of SDEs. At last, the theory is applied to a model problem and checked against results obtained by numerical experiments.