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The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics. (English) Zbl 1217.65174
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:
65M06Finite difference methods (IVP of PDE)
26A33Fractional derivatives and integrals (real functions)
35Q35PDEs in connection with fluid mechanics
35R11Fractional partial differential equations
45K05Integro-partial differential equations
76M20Finite difference methods (fluid mechanics)
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