@Article{JCM-37-3,
author = {Xinjie, Dai and Xiao, Aiguo},
title = {Numerical Solutions of Nonautonomous Stochastic Delay Differential Equations by Discontinuous Galerkin Methods},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {3},
pages = {419--436},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1806-m2017-0296},
url = {https://global-sci.com/article/84410/numerical-solutions-of-nonautonomous-stochastic-delay-differential-equations-by-discontinuous-galerkin-methods}
}