Abstract and Applied Analysis

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

Hengfei Ding and Changpin Li

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 493406, 15 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450400

Digital Object Identifier
doi:10.1155/2013/493406

Mathematical Reviews number (MathSciNet)
MR3081603

Zentralblatt MATH identifier
1291.65261

Citation

Ding, Hengfei; Li, Changpin. Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 493406, 15 pages. doi:10.1155/2013/493406. https://projecteuclid.org/euclid.aaa/1393450400


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