The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics

被引：68

作者：

Moaddy, K. ^{[2
]}

Momani, S. ^{[1
]}

Hashim, I. ^{[2
]}

机构：

[1] Univ Jordan, Fac Sci, Dept Math, Amman 11942, Jordan

[2] Univ Kebangsaan Malaysia, Sch Math Sci, Ukm Bangi Selangor 43600, Malaysia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 61卷 / 04期

关键词：

Non-standard finite difference schemes; Fractional differential equations; Telegraph equation; Wave equation; Burgers equation; EQUATIONS; CHAOS;

D O I：

10.1016/j.camwa.2010.12.072

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A non-standard finite difference scheme is developed to solve the linear partial differential equations with time- and space-fractional derivatives. The Grunwald-Letnikov method is used to approximate the fractional derivatives. Numerical illustrations that include the linear inhomogeneous time-fractional equation, linear space-fractional telegraph equation, linear inhomogeneous fractional Burgers equation and the fractional wave equation are investigated to show the pertinent features of the technique. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is very effective and convenient for solving linear partial differential equations of fractional order. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1209 / 1216

页数：8

共 27 条

[1]

[Anonymous], 1993, INTRO FRACTIONAL CA

[2]

[Anonymous], 2000, APPL NONSTANDARD FIN

[3]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[4]

BALEANU D., 2009, FRACTIONAL CALCULUS

[5] On the solution set for a class of sequential fractional differential equations [J].

Baleanu, Dumitru ;

Mustafa, Octavian G. ;

Agarwal, Ravi P. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (38)

[6] On the global existence of solutions to a class of fractional differential equations [J].

Baleanu, Dumitru ;

Mustafa, Octavian G. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (05) :1835-1841

[7] Analysis of fractional differential equations [J].

Diethelm, K ;

Ford, NJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 265 (02) :229-248

[8] Detailed error analysis for a fractional Adams method [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD .

NUMERICAL ALGORITHMS, 2004, 36 (01) :31-52

[9] A predictor-corrector approach for the numerical solution of fractional differential equations [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :3-22

[10] Numerical Bifurcation of Predator-Prey Fractional Differential Equations with a Constant Rate Harvesting [J].

Erjaee, G. H. .

ISND 2007: PROCEEDINGS OF THE 2007 INTERNATIONAL SYMPOSIUM ON NONLINEAR DYNAMICS, PTS 1-4, 2008, 96

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