Tempered fractional Laplacian is the generator of the tempered isotropic Lévy process. This paper provides the finite difference discretization for the two-dimensional tempered fractional Laplacian by using the weighted trapezoidal rule and the bilinear interpolation. Then it is used to solve the tempered fractional Poisson equation with homogeneous Dirichlet boundary condition and the error estimate is also derived. Numerical experiments verify the predicted convergence rates and effectiveness of the schemes.

中文翻译：

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二维回火分数拉普拉斯算子的算法实现与数值分析

回火分数拉普拉斯算子是回火各向同性 Lévy 过程的生成器。本文利用加权梯形规则和双线性插值对二维回火分数拉普拉斯算子进行了有限差分离散化。然后将其用于求解具有齐次Dirichlet边界条件的淬火分数Poisson方程，并推导出误差估计。数值实验验证了预测的收敛速度和方案的有效性。