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The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics
Moaddy K., , Hashim I.
Published in
2011
Volume: 61
   
Issue: 4
Pages: 1209 - 1216
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. © 2010 Elsevier Ltd. All rights reserved.
About the journal
JournalComputers and Mathematics with Applications
ISSN08981221
Open AccessNo