Volume 14, Issue 4
Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations

Adv. Appl. Math. Mech., 14 (2022), pp. 914-935.

Published online: 2022-04

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• 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.

65M10, 76M25

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@Article{AAMM-14-914, author = {}, title = {Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0018}, url = {http://global-sci.org/intro/article_detail/aamm/20440.html} }
TY - JOUR T1 - Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 914 EP - 935 PY - 2022 DA - 2022/04 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0018 UR - https://global-sci.org/intro/article_detail/aamm/20440.html KW - Lattice Boltzmann method, time-fractional wave equation, time-fractional Klein-Gordon equation, time-fractional Sine-Gordon equation. AB -

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.

Yibo Wang, Rui Du & Zhenhua Chai. (2022). Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations. Advances in Applied Mathematics and Mechanics. 14 (4). 914-935. doi:10.4208/aamm.OA-2021-0018
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