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

By J. Chen, F. Liu, V. Anh, S. Shen, Q. Liu and C. Liao

Abstract

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

Topics: 010301 Numerical Analysis, Fractional diffusion-wave equation with damping, Analytical solution, Implicit difference approximation, Stability, Convergence
Publisher: Elsevier
Year: 2012
DOI identifier: 10.1016/j.amc.2012.08.014
OAI identifier: oai:eprints.qut.edu.au:60021

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