NUMERICAL ANALYSIS FOR STOCHASTIC TIME-SPACE FRACTIONAL DIFFUSION EQUATION DRIVEN BY FRACTIONAL GAUSSIAN NOISE  

作　　者：Daxin Nie Weihua Deng 

机构地区：[1]School of Mathematics and Statistics,Gansu Key Laboratory of Applied Mathematics and Complex Systems,Lanzhou University,Lanzhou,China

出　　处：《Journal of Computational Mathematics》2024年第6期1502-1525,共24页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12071195,12301509,12225107);by the Innovative Groups of Basic Research in Gansu Province(Grant No.22JR5RA391);by the Major Science and Technology Projects in Gansu Province-Leading Talents in Science and Technology(Grant No.23ZDKA0005);by the Science and Technology Plan of Gansu Province(Grant No.22JR5RA535);by the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2023-pd04);by the China Postdoctoral Science Foundation(Grant No.2023M731466).

摘　　要：In this paper,we consider the strong convergence of the time-space fractional diffusion equation driven by fractional Gaussian noise with Hurst index H∈(1/2,1).A sharp regularity estimate of the mild solution and the numerical scheme constructed by finite element method for integral fractional Laplacian and backward Euler convolution quadrature for Riemann-Liouville time fractional derivative are proposed.With the help of inverse Laplace transform and fractional Ritz projection,we obtain the accurate error estimates in time and space.Finally,our theoretical results are accompanied by numerical experiments.

关 键 词：Fractional Laplacian Stochastic fractional diffusion equation Fractional Gaussian noise Finite element Convolution quadrature Error analysis 

分 类 号：O17[理学—数学]