A Finite-Difference Approximation for the One-and Two-Dimensional Tempered Fractional Laplacian

• 作 者: Yaoqiang Yan Weihua Deng Daxin Nie
• 机 构: School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex System
• 出 处: 应用数学与计算数学学报
• 发表日期: 2020年1期
• 关键词: Tempered fractional Laplacian Finite-difference scheme Linear and quadratic inte

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 lin-ear 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(h2-2s).