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 - <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>