Explicit Stabilized Multirate Method for Stiff Stochastic Differential Equations

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