Some high-order difference schemes for the distributed-order differential equations

被引：88

作者：

Gao, Guang-hua ^{[1
]}

Sun, Hai-wei ^{[2
]}

Sun, Zhi-zhong ^{[3
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210023, Jiangsu, Peoples R China

[2] Univ Macau, Dept Math, Macau, Peoples R China

[3] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2015年 / 298卷

基金：

中国国家自然科学基金;

关键词：

Distributed-order differential equations; High-order approximation; Fractional derivative; Difference scheme; Stability; Convergence; FRACTIONAL DIFFUSION EQUATION; ANOMALOUS SUBDIFFUSION EQUATION; NEUMANN BOUNDARY-CONDITIONS; HIGH SPATIAL ACCURACY; SUB-DIFFUSION; WAVE EQUATION; NUMERICAL-SOLUTION; APPROXIMATIONS; STABILITY; SYSTEM;

D O I：

10.1016/j.jcp.2015.05.047

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Two difference schemes are derived for both one-dimensional and two-dimensional distributed-order differential equations. It is proved that the schemes are unconditionally stable and convergent in an L-1(L-infinity) norm with the convergence orders O(tau(2)+ h(2)+ Delta alpha(2)) and O(tau(2)+ h(4)+ Delta alpha(4)) , respectively, where tau, h and Delta alpha are the step sizes in time, space and distributed-order variables. Several numerical examples are given to confirm the theoretical results. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：337 / 359

页数：23

共 38 条

[1]

Andreev V.B., 1976, DIFFERENCE METHODS E

[2] A high order schema for the numerical solution of the fractional ordinary differential equations [J].

Cao, Junying ;

Xu, Chuanju .

JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 238 :154-168

[3]

Caputo M., 1969, Elasticita e dissipazione

[4] A Fourier method for the fractional diffusion equation describing sub-diffusion [J].

Chen, Chang-Ming ;

Liu, F. ;

Turner, I. ;

Anh, V. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 227 (02) :886-897

[5] NUMERICAL SCHEMES WITH HIGH SPATIAL ACCURACY FOR A VARIABLE-ORDER ANOMALOUS SUBDIFFUSION EQUATION [J].

Chen, Chang-Ming ;

Liu, F. ;

Anh, V. ;

Turner, I. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (04) :1740-1760

[6] HIGH ORDER ALGORITHMS FOR THE FRACTIONAL SUBSTANTIAL DIFFUSION EQUATION WITH TRUNCATED LEVY FLIGHTS [J].

Chen, Minghua ;

Deng, Weihua .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2015, 37 (02) :A890-A917

[7] Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation [J].

Cui, Mingrong .

NUMERICAL ALGORITHMS, 2013, 62 (03) :383-409

[8] Compact finite difference method for the fractional diffusion equation [J].

Cui, Mingrong .

JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (20) :7792-7804

[9] Numerical analysis for distributed-order differential equations [J].

Diethelm, Kai ;

Ford, Neville J. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 225 (01) :96-104

[10]

Dimitrov Dim14 Yuri, 2014, J. Fract. Calc. Appl., V5

← 1 2 3 4 →