Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 71, Issue 9, Pages 1818-1830Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2016.02.024
Keywords
Fractional diffusion-wave equation; Fully discrete spectral method; Alternating direction implicit method; Semi-infinite channel; Error analysis
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Funding
- NSF of China [11272024]
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In this paper, we consider the numerical approximation of the time fractional diffusion-wave equation in a semi-infinite channel. The time fractional derivative is described in Caputo sense with order gamma (1 < gamma < 2). A fully discrete spectral scheme based on a finite difference method in the time direction and a Laguerre-Legendre spectral method in the space direction is proposed. We also propose an alternating direction implicit (ADI) spectral scheme in order to reduce the amount of computation. The stability and convergence of both schemes are rigorously established. Numerical results are presented to support our theoretical analysis. (C) 2016 Elsevier Ltd. All rights reserved.
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