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Zbl 1217.65174
Moaddy, K.; Momani, S.; Hashim, I.
The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics. (English)
[J] Comput. Math. Appl. 61, No. 4, 1209-1216 (2011). ISSN 0898-1221

Summary: 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.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
26A33 Fractional derivatives and integrals (real functions)
35Q35 Other equations arising in fluid mechanics
35R11
45K05 Integro-partial differential equations
76M20 Finite difference methods

Keywords: non-standard finite difference schemes; fractional differential equations; telegraph equation; wave equation; Burgers equation

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Zentralblatt MATH Berlin [Germany]