Analysis of the accuracy of numerical solutions of stochastic differential equations on supercomputers

Abstract

This paper investigated the accuracy of estimates of functionals of solutions of the CDS on supercomputers. It is shown that for accurate estimation of the expectation and variance of the solutions of linear SDE with multiplicative noise of the first and second order requires modeling ensembles of trajectories size 109 ? 1012, that can not be done on the PC because of the high labor intensity. Studied the behavior of the expectation and variance of the stochastic nonlinear solutions of the Van der Pol. Describes how to parallelize statistical algorithms on a multiprocessor cluster. The results of numerical experiments carried out on a supercomputer Siberian Supercomputer Center.