A Finite-Difference Approximation for the One- and Two-Dimensional Tempered Fractional Laplacian
A Finite-Difference Approximation for the One- and Two-Dimensional Tempered Fractional Laplacian
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DOI：
10.1007/s42967-019-00035-8
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发表时间：
2019-08
影响因子：
1.6
通讯作者：
Yaoqiang Yan;W. Deng;Daxin Nie
中科院分区：
文献类型：
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作者：
Yaoqiang Yan;W. Deng;Daxin Nie
本文给出了一维和二维回火分数阶拉普拉斯方程的有限差分离散化方法，并求解了具有齐次Dirichlet边界条件的回火分数阶泊松方程。其主要思想是分别用线性插值和二次插值逼近一维回火分数阶拉普拉斯算子的奇异性和非奇异性，用双线性插值和双二次插值逼近二维回火分数阶拉普拉斯算子。然后给出了截断误差并证明了收敛性。数值实验验证了该阶的收敛速度。
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.