MATHICSE Technical Report : Explicit stabilized multirate method for stiff stochastic differential equations

Stabilized explicit methods are particularly ecient for large systems of sti stochastic dif- ferential equations (SDEs) due to their extended stability domain. However, they loose their eciency when a severe stiness is induced by very few fast degrees of freedom, as the sti and nonsti terms are evaluated concurrently. Therefore, inspired by [A. Abdulle, M. J. Grote, and G. Rosilho de Souza, Preprint (2020), arXiv:2006.00744], we introduce a stochastic modi- ed equation whose stiness depends solely on the slow terms. By integrating this modied equation with a stabilized explicit scheme we devise a multirate method which overcomes the bottleneck caused by a few severely sti terms and recovers the eciency of stabilized schemes for large systems of nonlinear SDEs. The scheme is not based on any scale separation as- sumption of the SDE and therefore it is employable for problems stemming from the spatial discretization of stochastic parabolic partial dierential equations on locally rened grids. The multirate scheme has strong order 1=2, weak order 1 and its stability is proved on a model problem. Numerical experiments conrm the eciency and accuracy of the scheme.