EFFICIENT SPECTRAL METHODS FOR EIGENVALUE PROBLEMS OF THE INTEGRAL FRACTIONAL LAPLACIAN ONABALLOFANYDIMENSION  

作　　者：Suna Ma Huiyuan Li Zhimin Zhang Hu Chen Lizhen Chen 

机构地区：[1]College of Science,Nanjing University of Posts and Telecommunications,Nanjing,China [2]State Key Laboratory of Computer Science/Laboratory of Parallel Computing,Institute of Software,Chinese Academy of Sciences,Beijing,China [3]Department of Mathematics,Wayne State University,Detroit,USA [4]School of Mathematical Sciences,Ocean University of China,Qingdao,China [5]Beijing Computational Science Research Center,Beijing,China

出　　处：《Journal of Computational Mathematics》2024年第4期1032-1062,共31页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12101325)and by the NUPTSF(Grant No.NY220162);The second author was supported by the National Natural Science Foundation of China(Grant Nos.12131005,11971016);The third author was supported by the National Natural Science Foundation of China(Grant No.12131005);The fifth author was supported by the National Natural Science Foundation of China(Grant Nos.12131005,U2230402).

摘　　要：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 N4s 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 ob-tained.Numerical experiments are presented to demonstrate the accuracy and efficiency and to validate the theoretical results.

关 键 词：Integral fractional Laplacian Spectral method Eigenvalue problem Regularity analysis Error estimate 

分 类 号：O17[理学—数学]