Abstract
In this paper, a method based on radial basis function finite difference(RBF-FD) is developed for solving the time fractional convection-diffusion-wave equation(TFCDWE). We first approximate the equation by a scheme of order O(τ+h2), where τ,h are the time step size and spatial step size, respectively. We prove the stability and convergence of the discrete scheme, then the multiquadric RBF-FD approach is used to approximate the spatial derivatives. The aim of this paper is to show that the RBF-FD method is useful for solving our mentioned equation when the shape parameter selection is appropriate. The proposed method can be applied to complex domain, and has the advantages of mesh-free and simple procedure. Finally, numerical examples are proposed to verify the correctness of our previous theoretical analysis and to demonstrate the superiority of the RBF-FD method.
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