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 - <p style="text-align: justify;">Spectral and spectral collocation methods for tempered fractional diffusion
equations on the real line&nbsp;$\mathbb{R}$&nbsp;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.</p>