The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Chen, J., Liu, F., Anh, V., Shen, S., Liu, Q., & Liao, C. (2012) The analytical solution and numerical solution of the fractional diffusion-wave equation with damping. Applied Mathematics and Computation, 219(4), pp. 1737-1748.

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Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

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18 citations in Scopus
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20 citations in Web of Science®

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ID Code: 60021
Item Type: Journal Article
Refereed: Yes
Keywords: Fractional diffusion-wave equation with damping, Analytical solution, Implicit difference approximation, Stability, Convergence
DOI: 10.1016/j.amc.2012.08.014
ISSN: 0096-3003
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Elsevier Inc.
Deposited On: 16 May 2013 06:51
Last Modified: 22 Mar 2015 22:24

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