Algorithm implementation and numerical analysis for the two-dimensional tempered fractional Laplacian

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 te...

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Bibliographic Details
Published in:BIT 2021-12, Vol.61 (4), p.1421-1452
Main Authors: Sun, Jing, Nie, Daxin, Deng, Weihua
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Computational Mathematics and Numerical Analysis
Dirichlet problem
Finite difference method
Interpolation
Mathematics
Mathematics and Statistics
Numeric Computing
Numerical analysis
Poisson equation
Stochastic processes
Two dimensional analysis
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Summary: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.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-021-00860-5