Year: 2021
Author: Tengteng Cui, Sheng Chen, Yujian Jiao
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 1 : pp. 43–62
Abstract
Spectral and spectral collocation methods for tempered fractional diffusion equations on the real line $\mathbb{R}$ are developed. Applying the Fourier transform to the problem under consideration, we reduce it to systems of algebraic equations. Since Hermite functions are the eigenfunctions of the Fourier transform, they are used in the construction of spectral and spectral collocation methods for the algebraic equations obtained. The stability and convergence of the methods are studied. Numerical examples demonstrate the efficiency of the algorithms and confirm theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.070420.110720
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 1 : pp. 43–62
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Tempered fractional diffusion equation Hermite functions spectral method spectral collocation method problem on the whole line.