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Finite Difference Schemes for the Tempered Fractional Laplacian

Finite Difference Schemes for the Tempered Fractional Laplacian
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Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 2 : pp. 492–516

Abstract

The second and all higher order moments of the $\beta$-stable Lévy process diverge, the feature of which is sometimes referred to as shortcoming of the model when applied to physical processes. So a parameter $\lambda$ is introduced to exponentially temper the  Lévy process. The generator of the new process is tempered fractional Laplacian $(\Delta+\lambda)^{\beta/2}$ [W. H. Deng, B. Y. Li, W. Y. Tian and P. W. Zhang, Multiscale Model. Simul., 16(1), 125-149, 2018]. In this paper, we first design the finite difference schemes for the tempered fractional Laplacian equation with the generalized Dirichlet type boundary condition, their accuracy depending on the regularity of the exact solution on $\bar{\Omega}$. Then the techniques of effectively solving the resulting algebraic equation are presented, and the performances of the schemes are demonstrated by several numerical examples.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2017-0141

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 2 : pp. 492–516

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:   

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