An approximation scheme for the time fractional convection-diffusion equation

被引：34

作者：

Zhang, Juan ^{[1
]}

Zhang, Xindong ^{[1
]}

Yang, Bohui ^{[1
]}

机构：

[1] Xinjiang Normal Univ, Coll Math Sci, Urumqi 830017, Xinjiang, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 335卷

关键词：

Time fractional convection-diffusion equation; Caputo derivative; Stability; Convergence; Finite difference method; FINITE-ELEMENT-METHOD; PARTIAL-DIFFERENTIAL-EQUATION; NONLINEAR SOURCE-TERM; SPACE;

D O I：

10.1016/j.amc.2018.04.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a discrete form is proposed for solving time fractional convection-diffusion equation. Firstly, we obtain a time discrete scheme based on finite difference method. Secondly, we prove that the time discrete scheme is unconditionally stable, and the numerical solution converges to the exact one with order O(tau(2-infinity)), where tau is the time step size. Finally, two numerical examples are proposed respectively, to verify the order of convergence. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：305 / 312

页数：8

共 24 条

[1] Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations [J].

Bu, Weiping ;

Tang, Yifa ;

Yang, Jiye .

JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 276 :26-38

[2] A meshless local Petrov-Galerkin method for the time-dependent Maxwell equations [J].

Dehghan, Mehdi ;

Salehi, Rezvan .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 268 :93-110

[3] FINITE ELEMENT METHOD FOR THE SPACE AND TIME FRACTIONAL FOKKER-PLANCK EQUATION [J].

Deng, Weihua .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 47 (01) :204-226

[4] Application of collocation method for solving a parabolic-hyperbolic free boundary problem which models the growth of tumor with drug application [J].

Esmaili, Sakine ;

Eslahchi, M. R. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (05) :1711-1733

[5] High-order finite element methods for time-fractional partial differential equations [J].

Jiang, Yingjun ;

Ma, Jingtang .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (11) :3285-3290

[6] Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion [J].

Li, Changpin ;

Zhao, Zhengang ;

Chen, YangQuan .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) :855-875

[7] Finite difference/spectral approximations for the time-fractional diffusion equation [J].

Lin, Yumin ;

Xu, Chuanju .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 225 (02) :1533-1552

[8]

Ling LI, 2007, J CHONGQING U ARTS S, V26, P40

[9] Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation [J].

Liu, F. ;

Zhuang, P. ;

Anh, V. ;

Turner, I. ;

Burrage, K. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (01) :12-20

[10] An implicit RBF meshless approach for time fractional diffusion equations [J].

Liu, Q. ;

Gu, Y. T. ;

Zhuang, P. ;

Liu, F. ;

Nie, Y. F. .

COMPUTATIONAL MECHANICS, 2011, 48 (01) :1-12

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