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

This work addresses the numerical solution of tempered fractional PDEs, which are important for modeling anomalous diffusion, but the contribution is incremental as it extends existing finite difference methods to a specific operator.

This paper provides a finite difference discretization for the two-dimensional tempered fractional Laplacian and uses it to solve the tempered fractional Poisson equation with Dirichlet boundary conditions, deriving error estimates. Numerical experiments verify the convergence rates and effectiveness of the schemes.