Communications on Applied Mathematics and Computation ›› 2020, Vol. 2 ›› Issue (1): 129-145.doi: 10.1007/s42967-019-00035-8

• ORIGINAL PAPERS • 上一篇    下一篇

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

Yaoqiang Yan, Weihua Deng, Daxin Nie   

  1. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:2018-11-14 修回日期:2019-06-03 出版日期:2020-03-20 发布日期:2020-02-19
  • 通讯作者: Weihua Deng E-mail:dengwh@lzu.edu.cn
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China under Grant No. 11671182 and the Fundamental Research Funds for the Central Universities under Grant No. lzujbky-2018-ot03.

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

Yaoqiang Yan, Weihua Deng, Daxin Nie   

  1. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China
  • Received:2018-11-14 Revised:2019-06-03 Online:2020-03-20 Published:2020-02-19
  • Contact: Weihua Deng E-mail:dengwh@lzu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China under Grant No. 11671182 and the Fundamental Research Funds for the Central Universities under Grant No. lzujbky-2018-ot03.

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摘要： This paper provides a fnite-diference 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(h2-2s).

关键词: Tempered fractional Laplacian, Finite-diference scheme, Linear and quadratic interpolations, Bilinear and biquadratic interpolations, Convergence rates

Abstract: This paper provides a fnite-diference 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(h2-2s).

Key words: Tempered fractional Laplacian, Finite-diference scheme, Linear and quadratic interpolations, Bilinear and biquadratic interpolations, Convergence rates

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