TY - JOUR
T1 - Numerical Solutions of Nonautonomous Stochastic Delay Differential Equations by Discontinuous Galerkin Methods
AU - Dai , Xinjie
AU - Xiao , Aiguo
JO - Journal of Computational Mathematics
VL - 3
SP - 419
EP - 436
PY - 2018
DA - 2018/09
SN - 37
DO - http://doi.org/10.4208/jcm.1806-m2017-0296
UR - https://global-sci.org/intro/article_detail/jcm/12731.html
KW - Discontinuous Galerkin method, Wong-Zakai approximation, Nonautonomous
Stratonovich stochastic delay differential equation.
AB - <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>