Lattice Boltzmann Model for Time-Fractional NonlinearWave Equations

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.