线性随机分数阶延迟微分方程指数Euler-Maruyama方法的强收敛性  

STRONG CONVERGENCE OF THE EXPONENTIAL EULER-MARUYAMA METHOD FOR LINEAR CAPUTO STOCHASTIC FRACTIONAL DELAY DIFFERENTIAL EQUATIONS

作　　者：许珊珊 王琳[1] 王文强[1] Xu Shanshan;Wang Lin;Wang Wenqiang(Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Xiangtan 411105 China)

机构地区：[1]湘潭大学科学工程计算与数值仿真湖南省重点实验室,湘潭411105

出　　处：《高等学校计算数学学报》2022年第4期364-382,共19页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(12071403);湖南省教育厅重点项目(18A049)。

摘　　要：1引言近年来,分数阶延迟微分方程因其能够准确地描述反常次扩散现象、超反常扩散现象和多孔介质问题等在力学、物理、电气工程、控制理论等学科中的应用较为广泛.因此,研究者们针对该方程做了大量的研究且取得了丰富的研究成果,比如:2011年,Bhalekar和Daftardargejji[1]扩展了Adams-Bashforth-Moulton算法来求解分数阶延迟微分方程.This paper mainly studies the strong convergence of the exponential Euler-Maruyama method for a class of linear stochastic delay differential equations with Caputo time fractional derivative.Firstly,a suficient condition for the existence and uniqueness of the solution of the equation is given.Secondly,an exponential Euler-Maruyama method for numerically solving that equations is constructed.Then,it is proved that the strong convergence order of this method is α-1/2,(α∈(1/2,1).In particular,when α=1,the conclusions obtained are consistent with the results of the existing literature.Finally,the numerical example given at the end of the article verifies the correctness of the theoretical results obtained.

关 键 词：延迟微分方程 线性随机 强收敛性 反常扩散 分数阶 电气工程 扩散现象 多孔介质 

分 类 号：O242.28[理学—计算数学]