Error estimate of second-order finite difference scheme for solving the Riesz space distributed-order diffusion equation

被引：65

作者：

Abbaszadeh, Mostafa ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, 424 Hafez Ave, Tehran 15914, Iran

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 88卷

关键词：

Finite difference method; Riesz space distributed-order diffusion equation; Unconditional stability; Convergence; TIME-FRACTIONAL DIFFUSION; ACCURATE NUMERICAL-METHOD; WAVE-EQUATIONS;

D O I：

10.1016/j.aml.2018.08.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the current paper, an error estimate has been proposed to find a secondorder finite difference scheme for solving the Riesz space distributed-order diffusion equation. The convergence order of the proposed method is O(tau(2)+ h(2)). The numerical results show the efficiency of the new technique. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：179 / 185

页数：7

共 46 条

[1]

[Anonymous], 2014, ABSTR APPL ANAL

[2]

[Anonymous], 2001, Frac. Calc. Appl. Anal

[3]

[Anonymous], 2003, ANN GEOPHYS

[4] Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod [J].

Atanackovica, T. M. ;

Pilipovic, S. ;

Zorica, D. .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2011, 49 (02) :175-190

[5] An improved collocation method for multi-dimensional space-time variable-order fractional Schrodinger equations [J].

Bhrawy, A. H. ;

Zaky, M. A. .

APPLIED NUMERICAL MATHEMATICS, 2017, 111 :197-218

[6] A quadrature tau method for fractional differential equations with variable coefficients [J].

Bhrawy, A. H. ;

Alofi, A. S. ;

Ezz-Eldien, S. S. .

APPLIED MATHEMATICS LETTERS, 2011, 24 (12) :2146-2152

[7]

Caputo M., 1995, Ann. Univ. Ferrara, V41, P73, DOI [10.1007/BF02826009, DOI 10.1007/BF02826009]

[8] Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative [J].

Celik, Cem ;

Duman, Melda .

JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (04) :1743-1750

[9] Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations [J].

Chechkin, AV ;

Gorenflo, R ;

Sokolov, IM .

PHYSICAL REVIEW E, 2002, 66 (04) :7-046129

[10] A second-order accurate numerical method for the space-time tempered fractional diffusion-wave equation [J].

Chen, Minghua ;

Deng, Weihua .

APPLIED MATHEMATICS LETTERS, 2017, 68 :87-93

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