文献类型：期刊文献

英文题名：A numerical method for distributed order time fractional diffusion equation with weakly singular solutions

作者：Ren, Jincheng[1];Chen, Hu[2]

通讯作者：Chen, H[1]

机构：[1]Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450045, Henan, Peoples R China;[2]Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China.

年份：2019

卷号：96

起止页码：159-165

外文期刊名：APPLIED MATHEMATICS LETTERS

收录：;EI(收录号：20192006930513);Scopus(收录号：2-s2.0-85065577651);WOS:【SCI-EXPANDED(收录号:WOS:000472700700025)】；

基金：The research of this author is supported in part by the NSF of China (No. 11601119), sponsored by Program for HASTIT (No. 18HASTIT027) and Young talents Fund of HUEL.; The research of this author is supported in part by the Chinese Postdoc Foundation (No. 2018M631316) and the NSF of China (No. 11801026).

语种：英文

外文关键词：Distributed order derivative; L1 scheme; Weak singularity; Convergence analysis

摘要：A finite difference/spectral method is proposed for the numerical approximation of a distributed order time fractional diffusion equation with initial singularity on two dimensional spatial domain. The L1 scheme on graded mesh for the discretization of time Caputo fractional derivative is used to capture the weak initial singularity and Legendre spectral method is adopted for the spatial discretization. It is proved that with appropriate choice of the grading parameter, the scheme can attain order 2 - beta convergence in temporal direction, where beta (0 < beta < 1) is the upper bound of the order of distributed order fractional derivative. Numerical results confirm the sharpness of the error analysis. (C) 2019 Elsevier Ltd. All rights reserved.