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    Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

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    Type
    Article
    Authors
    Abdulle, Assyr
    Vilmart, Gilles
    Zygalakis, Konstantinos C.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2013-01
    Permanent link to this record
    http://hdl.handle.net/10754/600188
    
    Metadata
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    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.
    Sponsors
    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).
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Scientific Computing
    DOI
    10.1137/12088954X
    ae974a485f413a2113503eed53cd6c53
    10.1137/12088954X
    Scopus Count
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    Publications Acknowledging KAUST Support

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