For large-scale non-autonomous Stratonovich stochastic differential equations, we study a very general parallel waveform relaxation process which is on the basis of stochastic Runge–Kutta (SRK) method of mean-square order 1.0 in this literature. The convergence of the whole parallel numerical iterative scheme can be guaranteed and the scheme provides better properties in terms of decreasing the load of the computation and operating speed. At the same time, the related limit method is also introduced as the continuous approximation derived from the iterative scheme. In the approximation interval, it is worth noting that the mean-square order of the parallel numerical iterative scheme can be kept consistent with the previous SRK method at any arbitrary time point, not just at discrete points. Some numerical simulations are presented to elaborate the computing efficiency of the parallel numerical iterative scheme.

对于大型非自治Stratonovich随机微分方程，我们研究了一种非常通用的并行波形弛豫过程，该过程基于均方根1.0级随机Runge-Kutta（SRK）方法。可以保证整个并行数值迭代方案的收敛性，并且该方案在减少计算负荷和运算速度方面提供了更好的性能。同时，还引入了相关的极限方法作为从迭代方案中得出的连续逼近。在近似区间中，值得注意的是，并行数值迭代方案的均方阶数可以在任何任意时间点（而不仅仅是离散点）与以前的SRK方法保持一致。