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Original Articles

A Galerkin Finite Element Method to Solve Fractional Diffusion and Fractional Diffusion-Wave Equations

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Pages 260-273 | Received 18 May 2012, Accepted 06 Mar 2013, Published online: 12 Apr 2013
 

Abstract

In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L 2 and L are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.

AMS Subject Classification:

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