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 $(\Delta +\lambda {)}^{\frac{\beta }{2}}$. 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.

27 pages, 4 figures

References in corpus (6)

• A short FE implementation for a 2d homogeneous Dirichlet problem of a Fractional Laplacian
• Boundary problems for the fractional and tempered fractional operators
• A Riesz basis Galerkin method for the tempered fractional Laplacian
• Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting times
• Finite difference schemes for the tempered fractional Laplacian
• Finite difference methods for fractional Laplacians

Cited by in corpus (2)

• Numerical approximations for the tempered fractional Laplacian: Error analysis and applications
• Numerical methods for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion