Most approaches for computing numerically the solution of stochastic differential equations (SDEs) are based on time discrete approximation. In this paper, waveform relaxation (WR) methods are used to solve the linear SDE systems with multiplicative noise in the continuous time terms. The idea is to implement the WR methods by splitting the drift coefficient of the SDE at the equation level and to solve for different subcomponents of the system independently using previous iterates as inputs. In particular, comparisons between the speed of convergence in the mean square sense of the WR iterations of various modes of block Jacobi, block Gauss-Seidel and block SOR methods are shown and numerical results are presented to illustrate the theory.

MINISIMPOSIUM SESSION: 7. Numerical methods for Stochastic equations