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

Authors:
K. Moaddy;S. Momani;I. Hashim
Affiliations:
School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia;Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan;School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 3
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Abstract

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.