@Article{AAMM-14-914,
author = {Yibo Wang, Rui Du and Zhenhua Chai},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0018},
url = {http://global-sci.org/intro/article_detail/aamm/20440.html}
}