Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

Type

Article

Authors

Abdulle, Assyr
Vilmart, Gilles
Zygalakis, Konstantinos C.

KAUST Grant Number

KUK-C1-013-04

Date

2013-01

Abstract

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Citation

Abdulle A, Vilmart G, Zygalakis KC (2013) Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations. SIAM Journal on Scientific Computing 35: A1792–A1814. Available: http://dx.doi.org/10.1137/12088954X.

Acknowledgements

This author's work was partially supported by Swiss National Foundation Grant 200021_140692.This author's work was partially supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).