Volume 11, Issue 1
Efficient Hermite Spectral Methods for Space Tempered Fractional Diffusion Equations

East Asian J. Appl. Math., 11 (2021), pp. 43-62.

Published online: 2020-11

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• 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.

• Keywords

Tempered fractional diffusion equation, Hermite functions, spectral method, spectral collocation method, problem on the whole line.

65N35, 65E05, 65M70, 41A05, 41A10, 41A25

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@Article{EAJAM-11-43, author = {Tengteng and Cui and and 9648 and and Tengteng Cui and Sheng and Chen and and 9649 and and Sheng Chen and Yujian and Jiao and and 9650 and and Yujian Jiao}, title = {Efficient Hermite Spectral Methods for Space Tempered Fractional Diffusion Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {11}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070420.110720}, url = {http://global-sci.org/intro/article_detail/eajam/18412.html} }
TY - JOUR T1 - Efficient Hermite Spectral Methods for Space Tempered Fractional Diffusion Equations AU - Cui , Tengteng AU - Chen , Sheng AU - Jiao , Yujian JO - East Asian Journal on Applied Mathematics VL - 1 SP - 43 EP - 62 PY - 2020 DA - 2020/11 SN - 11 DO - http://doi.org/10.4208/eajam.070420.110720 UR - https://global-sci.org/intro/article_detail/eajam/18412.html KW - Tempered fractional diffusion equation, Hermite functions, spectral method, spectral collocation method, problem on the whole line. AB -

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.

Tengteng Cui, Sheng Chen & Yujian Jiao. (2020). Efficient Hermite Spectral Methods for Space Tempered Fractional Diffusion Equations. East Asian Journal on Applied Mathematics. 11 (1). 43-62. doi:10.4208/eajam.070420.110720
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