Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

We introduce a new family of explicit integrators for stiff Itoî 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 exp...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2013-01, Vol.35 (4), p.A1792-A1814
Main Authors: Abdulle, Assyr, Vilmart, Gilles, Zygalakis, Konstantinos C
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Asymptotic properties
Convergence
Differential equations
Mathematics
Methods
Nonlinearity
Numerical Analysis
Random variables
Stability
Stochasticity
Values
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Summary:We introduce a new family of explicit integrators for stiff Itoî 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, mean-square, 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. [PUBLICATION ABSTRACT]
ISSN:1064-8275
1095-7197
DOI:10.1137/12088954X