A High-Precision Meshless Method for Time-Fractional Mixed Diffusion and Wave Equations

In this paper, a meshless scheme based on Kernel Derivative Free Smoothed Particle Hydrodynamics (KDF-SPH) approximation is proposed to solve the time-fractional mixed diffusion and wave equations. The time fractional derivative is defined in the Caputo sense, and we use the finite difference method to discretize. The meshless method based on KDF-SPH is used for spatial discretization. Thus, a fully discrete meshless numerical scheme is obtained. At the same time, we use the obtained meshless discrete scheme to solve the initial boundary value problems of time-fractional mixed diffusion and wave equations in regular and irregular regions, and we get good results. By comparing the proposed method with many numerical methods, the accuracy and effectiveness of the proposed method are further verified.