Numerical Solutions of Nonautonomous Stochastic Delay Differential Equations by Discontinuous Galerkin Methods

Numerical Solutions of Nonautonomous Stochastic Delay Differential Equations by Discontinuous Galerkin Methods

Year:    2019

Author:    Xinjie Dai, Aiguo Xiao

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 3 : pp. 419–436

Abstract

This paper considers a class of discontinuous Galerkin method, which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis, for numerically solving nonautonomous Stratonovich stochastic delay differential equations. We prove that the discontinuous Galerkin scheme is strongly convergent, globally stable and analogously asymptotically stable in mean square sense. In addition, this method can be easily extended to solve nonautonomous Stratonovich stochastic pantograph differential equations. Numerical tests indicate that the method has first-order and half-order strong mean square convergence, when the diffusion term is without delay and with delay, respectively.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1806-m2017-0296

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 3 : pp. 419–436

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Discontinuous Galerkin method Wong-Zakai approximation Nonautonomous Stratonovich stochastic delay differential equation.

Author Details

Xinjie Dai

Aiguo Xiao

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