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

K. Moaddy, S. Momani, Ishak Hashim

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

A non-standard finite difference scheme is developed to solve the linear partial differential equations with time- and space-fractional derivatives. The GrunwaldLetnikov 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.

Original languageEnglish
Pages (from-to)1209-1216
Number of pages8
JournalComputers and Mathematics with Applications
Volume61
Issue number4
DOIs
Publication statusPublished - Feb 2011

Fingerprint

Nonstandard Finite Difference Schemes
Fluid Mechanics
Fluid mechanics
Linear equations
Partial differential equations
Fractional
Derivatives
Telegraph
Linear partial differential equation
Fractional Derivative
Wave equations
Telegraph Equation
Fractional Order
Burgers Equation
Linear Space
Wave equation
Numerical Results

Keywords

  • Burgers equation
  • Fractional differential equations
  • Non-standard finite difference schemes
  • Telegraph equation
  • Wave equation

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Modelling and Simulation
  • Computational Mathematics

Cite this

The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics. / Moaddy, K.; Momani, S.; Hashim, Ishak.

In: Computers and Mathematics with Applications, Vol. 61, No. 4, 02.2011, p. 1209-1216.

Research output: Contribution to journalArticle

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