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

页码：923 / 939

页数：17

共 50 条

[1] An alternating direction implicit Galerkin finite element method for the distributed-order time-fractional mobile-immobile equation in two dimensions [J].

Qiu, Wenlin ;

Xu, Da ;

Chen, Haifan ;

Guo, Jing .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (12) :3156-3172

[2] A Radial Basis Function-Hermite Finite Difference Method for the Two-Dimensional Distributed-Order Time-Fractional Cable Equation [J].

Haghi, Majid ;

Ilati, Mohammad .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025, 48 (06) :6573-6585

[3] Utilizing differential quadrature-based RBF partition of unity collocation method to simulate distributed-order time fractional Cable equation [J].

Biranvand, Nader ;

Ebrahimijahan, Ali .

COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (01)

[4] A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation [J].

Zhang, Yaping ;

Cao, Jiliang ;

Bu, Weiping ;

Xiao, Aiguo .

INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING, 2020, 11 (02)

[5] A Galerkin finite element method for the modified distributed-order anomalous sub-diffusion equation [J].

Li, Lang ;

Liu, Fawang ;

Feng, Libo ;

Turner, Ian .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 368

[6] Utilizing differential quadrature-based RBF partition of unity collocation method to simulate distributed-order time fractional Cable equation [J].

Nader Biranvand ;

Ali Ebrahimijahan .

Computational and Applied Mathematics, 2024, 43

[7] A novel finite volume method for the Riesz space distributed-order diffusion equation [J].

Li, J. ;

Liu, F. ;

Feng, L. ;

Turner, I. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (04) :772-783

[8] High-Order Numerical Method for Solving a Space Distributed-Order Time-Fractional Diffusion Equation [J].

Li, Jing ;

Yang, Yingying ;

Jiang, Yingjun ;

Feng, Libo ;

Guo, Boling .

ACTA MATHEMATICA SCIENTIA, 2021, 41 (03) :801-826

[9] A NUMERICAL METHOD FOR TWO-DIMENSIONAL DISTRIBUTED-ORDER FRACTIONAL NONLINEAR SOBOLEV EQUATION [J].

Zhagharian, Sh. ;

Heydari, M. H. ;

Razzaghi, M. .

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2023, 13 (05) :2630-2645

[10] A numerical method for distributed-order time fractional 2D Sobolev equation [J].

Heydari, M. H. ;

Rashid, S. ;

Jarad, F. .

RESULTS IN PHYSICS, 2023, 45

← 1 2 3 4 5 →