Algorithm implementation and numerical analysis for the two-dimensional tempered fractional Laplacian

Tempered fractional Laplacian is the generator of the tempered isotropic Levy process. This paper provides the finite difference discretization for the two-dimensional tempered fractional Laplacian by using the weighted trapezoidal rule and the bilinear interpolation. Then it is used to solve the tempered fractional Poisson equation with homogeneous Dirichlet boundary condition and the error estimate is also derived. Numerical experiments verify the predicted convergence rates and effectiveness of the schemes.