NUMERICAL SOLUTIONS OF NONAUTONOMOUS STOCHASTIC DELAY DIFFERENTIAL EQUATIONS BY DISCONTINUOUS GALERKIN METHODS  

作　　者：Xinjie Dai Aiguo Xiao 

机构地区：[1]School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China [2]School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Xiangtan 411105,China

出　　处：《Journal of Computational Mathematics》2019年第3期419-436,共18页计算数学（英文）

基　　金：the National Natural Science Foundation of China(No.11671343).

摘　　要：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.

关 键 词：DISCONTINUOUS GALERKIN method Wong-Zakai APPROXIMATION NONAUTONOMOUS Stratonovich stochastic delay differential equation 

分 类 号：O1[理学—数学]