@Article{JCM-42-4,
author = {Suna, Ma and Li, Huiyuan and Zhimin, Zhang and Hu, Chen and Lizhen, Chen},
title = {Efficient Spectral Methods for Eigenvalue Problems of the Integral Fractional Laplacian on a Ball of Any Dimension},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {4},
pages = {1032--1062},
abstract = {<p style="text-align: justify;">An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional
Laplacian on a unit ball of any dimension is proposed in this paper. The symmetric positive
definite linear system is retained explicitly which plays an important role in the numerical
analysis. And a sharp estimate on the algebraic system’s condition number is established
which behaves as $N^{4s}$ with respect to the polynomial degree $N,$ where $2s$ is the fractional
derivative order. The regularity estimate of solutions to source problems of the fractional
Laplacian in arbitrary dimensions is firstly investigated in weighted Sobolev spaces. Then
the regularity of eigenfunctions of the fractional Laplacian eigenvalue problem is readily
derived. Meanwhile, rigorous error estimates of the eigenvalues and eigenvectors are obtained. Numerical experiments are presented to demonstrate the accuracy and efficiency
and to validate the theoretical results.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2304-m2022-0243},
url = {https://global-sci.com/article/91087/efficient-spectral-methods-for-eigenvalue-problems-of-the-integral-fractional-laplacian-on-a-ball-of-any-dimension}
}