Lattice Boltzmann Model for Time-Fractional Nonlinear Wave Equations (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, a lattice Boltzmann model with BGK operator (LBGK) for solving time-fractional nonlinear wave equations in Caputo sense is proposed. First, theCaputo fractional derivative is approximated using the fast evolution algorithm basedon the sum-of-exponentials approximation. Then the target equation is transformedinto an approximate form, and for which a LBGK model is developed. Throughthe Chapman-Enskog analysis, the macroscopic equation can be recovered from thepresent LBGK model. In addition, the proposed model can be extended to solve thetime-fractional Klein-Gordon equation and the time-fractional Sine-Gordon equation.Finally, several numerical examples are performed to show the accuracy and efficiencyof the present LBGK model. From the numerical results, the present model has asecond-order accuracy in space.