Modified Galerkin Method for Derivative Dependent Fredholm–Hammerstein Integral Equations of Second Kind
Year: 2024
Author: Kapil Kant, Payel Das, Gnaneshwar Nelakanti, Ratish Kumar
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 4 : pp. 905–926
Abstract
In this paper, we consider modified Galerkin and iterated modified Galerkin methods for solving a class of two point boundary value problems. The methods are applied after constructing the equivalent derivative dependent Fredholm-Hammerstein integral equations to the boundary value problem. Existence and convergence of the approximate solutions to the actual solution is discussed and the rates of convergence are obtained. Superconvergence results for the approximate and iterated approximate solutions of piecewise polynomial based modified Galerkin method in infinity norm are given. We have also established that iterated modified Galerkin approximation improves over the modified Galerkin solution. Numerical examples are presented to illustrate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0277
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 4 : pp. 905–926
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Fredholm integral equations Green’s kernel modified Galerkin method piecewise polynomial superconvergence rates.