Algorithm Implementation And Numerical Analysis For The Two-dimensional Tempered Fractional Laplacian

Tempered fractional Laplacian is the generator of the tempered isotropic Lévy pro-cess.In this paper,we provide a finite difference scheme by discretizing the tempered fractional Laplacian??+???/2.We prove that for ??²????²?,the accuracy is O(?^2-?).Moreover,we solve the tempered fractional Poisson equation with Dirichlet boundary conditions and derive the error estimates for the present method.Numerical experiments verify the expected convergence rates.