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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 493406, 15 pages
http://dx.doi.org/10.1155/2013/493406
Research Article

Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 24 April 2013; Revised 24 June 2013; Accepted 24 June 2013

Academic Editor: Juan J. Trujillo

Copyright © 2013 Hengfei Ding and Changpin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Two numerical algorithms are derived to compute the fractional diffusion-wave equation with a reaction term. Firstly, using the relations between Caputo and Riemann-Liouville derivatives, we get two equivalent forms of the original equation, where we approximate Riemann-Liouville derivative by a second-order difference scheme. Secondly, for second-order derivative in space dimension, we construct a fourth-order difference scheme in terms of the hyperbolic-trigonometric spline function. The stability analysis of the derived numerical methods is given by means of the fractional Fourier method. Finally, an illustrative example is presented to show that the numerical results are in good agreement with the theoretical analysis.