Year: 2022
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 4 : pp. 914–935
Abstract
In this paper, a lattice Boltzmann model with BGK operator (LBGK) for solving time-fractional nonlinear wave equations in Caputo sense is proposed. First, the Caputo fractional derivative is approximated using the fast evolution algorithm based on the sum-of-exponentials approximation. Then the target equation is transformed into an approximate form, and for which a LBGK model is developed. Through the Chapman-Enskog analysis, the macroscopic equation can be recovered from the present LBGK model. In addition, the proposed model can be extended to solve the time-fractional Klein-Gordon equation and the time-fractional Sine-Gordon equation. Finally, several numerical examples are performed to show the accuracy and efficiency of the present LBGK model. From the numerical results, the present model has a second-order accuracy in space.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0018
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 4 : pp. 914–935
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Lattice Boltzmann method time-fractional wave equation time-fractional Klein-Gordon equation time-fractional Sine-Gordon equation.
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