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Implicit Difference Scheme of the Space-Time Fractional Advection Diffusion Equation

E. A. Abdel-Rehim

Abstract

The space-time fractional advection diffusion equations are linear partial pseudo-differential equation with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. We use the implicit difference scheme, the theta-method, to find the approximation solution of these equations in the long run. The proofs of stability of the difference scheme of each models are given. We compare the numerical results of these models for different values of the space and the time fractional orders and for different values of theta.

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Received: 2014-12-1
Revised: 2015-8-19
Published Online: 2015-12-5
Published in Print: 2015-12-1

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