Nonpolynomial Jacobi Spectral-Collocation Method for Weakly Singular Fredholm Integral Equations of the Second Kind
Year: 2024
Author: Qiumei Huang, Min Wang
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 4 : pp. 927–951
Abstract
In this paper a nonpolynomial Jacobi spectral-collocation (NJSC) method for the second kind Fredholm integral equations (FIEs) with weakly singular kernel $|s−t|^{−\gamma}$ is proposed. By dividing the integral interval symmetrically into two parts and applying the NJSC method symmetrically to the two weakly singular FIEs respectively, the mild singularities of the interval endpoints can be captured and the exponential convergence can be obtained. A detailed $L^∞$ convergence analysis of the numerical solution is derived. The NJSC method is then extended to two dimensional case and similar exponential convergence results are obtained for low regular solutions. Numerical examples are presented to demonstrate the efficiency of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0341
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 4 : pp. 927–951
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Nonpolynomial Jacobi spectral-collocation method Fredholm integral equations weakly singular exponential convergence.
Author Details
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https://doi.org/10.1016/j.apnum.2024.08.003 [Citations: 0]