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

Abstract

Tempered fractional Laplacian is the generator of the tempered isotropic Lévy process [W.H. Deng, B.Y. Li, W.Y. Tian, and P.W. Zhang, Multiscale Model. Simul., 16(1), 125-149, 2018]. This paper provides the finite difference discretization for the two dimensional tempered fractional Laplacian $(Δ+λ)^{\fracβ{2}}$. Then we use it to solve the tempered fractional Poisson equation with Dirichlet boundary conditions and derive the error estimates. Numerical experiments verify the convergence rates and effectiveness of the schemes.