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
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