Year: 2024
Author: Tao Sun, Hai-Wei Sun
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 3 : pp. 697–726
Abstract
In this paper, we investigate the numerical solution of the two-dimensional fractional Laplacian wave equations. After splitting out the Riesz fractional derivatives from the fractional Laplacian, we treat the Riesz fractional derivatives with an implicit scheme while solving the rest part explicitly. Thanks to the tensor structure of the Riesz fractional derivatives, a splitting alternative direction implicit (S-ADI) scheme is proposed by incorporating an ADI remainder. Then the Gohberg-Semencul formula, combined with fast Fourier transform, is proposed to solve the derived Toeplitz linear systems at each time integration. Theoretically, we demonstrate that the S-ADI scheme is unconditionally stable and possesses second-order accuracy. Finally, numerical experiments are performed to demonstrate the accuracy and efficiency of the S-ADI scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2023-0149
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 3 : pp. 697–726
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Operator splitting alternative direction implicit scheme Gohberg-Semencul formula fractional Laplacian wave equation.