This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.T...This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.The main ideas are to,respectively,use linear and quadratic interpolations to approximate the singularity and non-singularity of the one-dimensional tempered fractional Laplacian and bilinear and biquadratic interpolations to the two-dimensional tempered fractional Laplacian.Then,we give the truncation errors and prove the convergence.Numerical experiments verify the convergence rates of the order O(h^2−2s).展开更多
基金the National Natural Science Foundation of China under Grant No.11671182the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2018-ot03.
文摘This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.The main ideas are to,respectively,use linear and quadratic interpolations to approximate the singularity and non-singularity of the one-dimensional tempered fractional Laplacian and bilinear and biquadratic interpolations to the two-dimensional tempered fractional Laplacian.Then,we give the truncation errors and prove the convergence.Numerical experiments verify the convergence rates of the order O(h^2−2s).
