A novel finite element method for the distributed-order time fractional Cable equation in two dimensions

被引：24
作者：
Gao, Xinghua [1 ]
Liu, Fawang [2 ,3 ,4 ]
Li, Hong [1 ]
Liu, Yang [1 ]
Turner, Ian [2 ,5 ]
Yin, Baoli [1 ]
机构：
[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia
[3] Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350116, Fujian, Peoples R China
[4] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China
[5] Queensland Univ Technol QUT, Australian Res Council Ctr Excellence Math & Stat, Brisbane, Qld, Australia
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 80卷 / 05期
基金：
中国国家自然科学基金; 澳大利亚研究理事会;
关键词：
Galerkin finite element method; Irregular convex domains; Distributed-order time fractional Cable equation; Composite Trapezoid formula; DIFFUSION-WAVE EQUATION; SPECTRAL METHOD; DIFFERENCE APPROXIMATIONS; NUMERICAL-METHODS; VOLUME METHOD; SCHEME;
D O I：
10.1016/j.camwa.2020.04.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the unstructured mesh Galerkin finite element method with a weighted and shifted Grunwald difference approximation and Composite Trapezoid formula is presented to solve the nonhomogeneous two-dimensional distributed order time fractional Cable equation on irregular convex domains. The Crank-Nicolson type discretization of the finite element scheme is implemented to obtain the numerical solution. The stability and convergence of the numerical scheme are discussed and derived. Finally, some numerical examples on irregular convex domains are given to confirm our theoretical results. (C) 2020 Elsevier Ltd. All rights reserved.
引用
收藏
页码：923 / 939
页数：17
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