A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels  

作　　者：Chao Zhang Guoqing Yao Sheng Chen 

机构地区：[1]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,China [2]School of Science,University of Shanghai for Science and Technology,Shanghai 200093,China [3]Research Center for Mathemaics,Beijing Normal University,Zhuhai 519087,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2022年第4期1041-1062,共22页高等学校计算数学学报（英文版）

基　　金：The research of C.Zhang is partially supported by NSFC(Grant Nos.11971207,12071172);the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.20KJA11002);The research of S.Chen is partially supported by NSFC(Grant No.11801235).

摘　　要：In this paper,we propose a hybrid spectral method for a type of nonlocal problems,nonlinear Volterra integral equations(VIEs)of the second kind.The main idea is to use the shifted generalized Log orthogonal functions(GLOFs)as the basis for the first interval and employ the classical shifted Legendre polynomials for other subintervals.This method is robust for VIEs with weakly singular kernel due to the GLOFs can efficiently approximate one-point singular functions as well as smooth functions.The well-posedness and the related error estimates will be provided.Abundant numerical experiments will verify the theoretical results and show the high-efficiency of the new hybrid spectral method.

关 键 词：Nonlocal problem Volterra integral spectral element method log orthogonal function Legendre polynomial weak singularity exponential convergence 

分 类 号：O17[理学—数学]