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Tempered fractional Laplacian is the generator of the tempered isotropicL\'evy process [W.H. Deng, B.Y. Li, W.Y. Tian, and P.W. Zhang, MultiscaleModel. Simul., 16(1), 125-149, 2018]. This paper provides the finite differencediscretization for the two dimensional tempered fractional Laplacian$(\Delta+\lambda)^{\frac{\beta}{2}}$. Then we use it to solve the temperedfractional Poisson equation with Dirichlet boundary conditions and derive theerror estimates. Numerical experiments verify the convergence rates andeffectiveness of the schemes.

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