Year: 2022
Author: Guoqing Yao, Chao Zhang, Sheng Chen, Guoqing Yao, Sheng Chen
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 4 : pp. 1041–1062
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0006s
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 4 : pp. 1041–1062
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Nonlocal problem Volterra integral spectral element method log orthogonal function Legendre polynomial weak singularity exponential convergence.