Superconvergent method for weakly singular Fredholm-Hammerstein integral equations with non-smooth solutions and its application

In this article, we propose shifted Jacobi spectral Galerkin method (SJSGM) and iterated SJSGM to solve nonlinear Fredholm integral equations of Hammerstein type with weakly singular kernel. We have rigorously studied convergence analysis of the proposed methods. Even though the exact solution exhib...

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Vydáno v:Applied numerical mathematics Ročník 207; s. 24 - 44
Hlavní autoři: Kayal, Arnab, Mandal, Moumita
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.01.2025
Témata:
Fredholm-Hammerstein integral equation
Jacobi spectral Galerkin method
Non-smooth solution
Superconvergence
Weakly singular kernel
Superconvergence
Jacobi spectral Galerkin method
Fredholm-Hammerstein integral equation
Weakly singular kernel
Non-smooth solution
ISSN:0168-9274
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Shrnutí:In this article, we propose shifted Jacobi spectral Galerkin method (SJSGM) and iterated SJSGM to solve nonlinear Fredholm integral equations of Hammerstein type with weakly singular kernel. We have rigorously studied convergence analysis of the proposed methods. Even though the exact solution exhibits non-smooth behaviour, we manage to achieve superconvergence order for the iterated SJSGM. Further, using smoothing transformation, we improve the regularity of the exact solution, which enhances the convergence order of the SJSGM and iterated SJSGM. We have also shown the applicability of our proposed methods to high-order nonlinear weakly singular integro-differential equations and achieved superconvergence. Several numerical examples have been implemented to demonstrate the theoretical results.
ISSN:0168-9274
DOI:10.1016/j.apnum.2024.08.018