Numerical Solutions of Nonautonomous Stochastic Delay Differential Equations by Discontinuous Galerkin Methods (Journal of Computational Mathematics, 2019)
This paper considers a class of discontinuous Galerkin method, which is constructedby Wong-Zakai approximation with the orthonormal Fourier basis, for numerically solvingnonautonomous Stratonovich stochastic delay differential equations. We prove thatthe discontinuous Galerkin scheme is strongly convergent, globally stable and analogouslyasymptotically stable in mean square sense. In addition, this method can be easily extendedto solve nonautonomous Stratonovich stochastic pantograph differential equations.Numerical tests indicate that the method has first-order and half-order strong mean squareconvergence, when the diffusion term is without delay and with delay, respectively.
Keywords: Discontinuous Galerkin method; Wong-Zakai approximation; Nonautonomous Stratonovich stochastic delay differential equation.