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Compact implicit difference approximation for time-fractional diffusion-wave equation
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DOI：10.1016/j.aej.2021.09.005.png)
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Abstract
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In this article, developed the compact implicit difference method based Grunwald Letnikov formula (GLF) to compute the solution of the time-fractional diffusion-wave equation (TFDWE) describing wave propagation phenomenan having order alpha (1 < alpha < 2). The fractional derivative is in Caputo sense. The theoretical analysis such as stability, consistency, convergence and solvability of the said scheme are discussed and proved that the scheme is conditionally stable and convergent with the order (tau(2) (Delta x)(4)). The numerical results compared with the recent existed method. The results of the numerical examples show that the GLF and the proposed method is very accurate and efficient for time fractional diffusion-wave equation. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
Keywords:
Compact approximation
Implicit difference scheme
Fractional diffusion-wave equation
Grtinwald Letnikov formula
Stability
Consistency
Convergence
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