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...

Full description

Saved in:

Bibliographic Details
Published in:	Applied numerical mathematics Vol. 207; pp. 24 - 44
Main Authors:	Kayal, Arnab, Mandal, Moumita
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.01.2025
Subjects:	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
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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