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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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