Local discontinuous Galerkin method for distributed‐order time‐fractional diffusion‐wave equation: Application of Laplace transform

In this paper, the Laplace transform combined with the local discontinuous Galerkin method is used for distributed‐order time‐fractional diffusion‐wave equation. In this method, at first, we convert the equation to some time‐independent problems by Laplace transform. Then, we solve these stationary...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-04, Vol.44 (6), p.4923-4937
Main Authors: Mohammadi‐Firouzjaei, Hadi, Adibi, Hojatollah, Dehghan, Mehdi
Format: Article
Language:English
Subjects:
Diffusion
distributed‐order time‐fractional diffusion‐wave equation
Galerkin method
Laplace transform
Laplace transforms
local discontinuous Galerkin method
Numerical methods
parallel algorithms
Wave equations
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Summary:In this paper, the Laplace transform combined with the local discontinuous Galerkin method is used for distributed‐order time‐fractional diffusion‐wave equation. In this method, at first, we convert the equation to some time‐independent problems by Laplace transform. Then, we solve these stationary equations by the local discontinuous Galerkin method to discretize diffusion operators at the same time. Next, by using a numerical inversion of the Laplace transform, we find the solution of the original equation. One of the advantages of this procedure is its capability to be implemented in a parallel environment. It's another advantage is that the number of stationary problems that should be solved is much less than that is needed in time‐marching methods. Finally, some numerical experiments have been provided to show the accuracy and efficiency of the method.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7077