Adv. Appl. Math. Mech., 14 (2022), pp. 914-935.
Published online: 2022-04
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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} }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.