A meshless particle method for solving time-fractional wave equations

In this paper, an accurate meshless method for solving time-fractional wave equation (TFWE) based on KDF-SPH approximation is proposed. In this method, finite difference method is used to discretize the time-fractional derivative defined in the Caputo sense. The spatial discretization is achieved using KDF-SPH meshless method. At the same time, the kernel approximation and particle approximation expressions are given. In order to prove the effectiveness and order of numerical convergence of the proposed method, a number of 1D and 2D initial boundary value problems are numerically simulated in regular and irregular domains, and the meshless method is compared with the existing methods. Numerical results show the effectiveness and accuracy of the proposed method, and the second-order accuracy is achieved in space in the regular calculation area.