Close Search Advanced
Journals
Resources
About Us
Open Access

Efficient Hermite Spectral Methods for Space Tempered Fractional Diffusion Equations

Efficient Hermite Spectral Methods for Space Tempered Fractional Diffusion Equations
Preview
Add to basket

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.

Submit Article

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/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.

Author Details

Tengteng Cui

Sheng Chen

Yujian Jiao

  1. Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations

    Li, Shu-Jiao | Lu, Kang-Ya | Miao, Cun-Qiang

    Numerical Algorithms, Vol. (2024), Iss.

    https://doi.org/10.1007/s11075-024-01817-9 [Citations: 0]

  2. Tempered fractional Jacobi-Müntz basis for image reconstruction application and high-order pseudospectral tempered fractional differential matrices

    Dahy, Sayed A. | El-Hawary, H.M. | Fahim, Alaa | Farhat, Amal A.

    Applied Mathematics and Computation, Vol. 481 (2024), Iss. P.128954

    https://doi.org/10.1016/j.amc.2024.128954 [Citations: 0]

  3. Spectral Solutions for Fractional Black–Scholes Equations

    Abdelkawy, M. A. | Lopes, António M. | Muhammad, Taseer

    Mathematical Problems in Engineering, Vol. 2022 (2022), Iss. P.1

    https://doi.org/10.1155/2022/9365292 [Citations: 4]