Superconvergent scheme for a system of Green nonlinear Fredholm integral equations

This study investigates a system of second-kind nonlinear Fredholm integral equations (SSNFIEs) featuring a Green's type kernel function. To solve this integral equations (IEs), we introduce Galerkin and iterated Galerkin (IG) methods based on piecewise polynomials. Convergence and error analys...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 479; p. 128880
Main Authors Kumar, Rakesh, Rathish Kumar, B.V.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.10.2024
Subjects
Fredholm integral equation
Galerkin method
Green kernel
Iterated Galerkin method
Galerkin method
Green kernel
Iterated Galerkin method
Fredholm integral equation
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Summary:This study investigates a system of second-kind nonlinear Fredholm integral equations (SSNFIEs) featuring a Green's type kernel function. To solve this integral equations (IEs), we introduce Galerkin and iterated Galerkin (IG) methods based on piecewise polynomials. Convergence and error analysis are conducted for these methods, and we demonstrate superconvergence for the IG method. Numerical tests are employed to validate the theoretical findings. •A system of second-kind coupled nonlinear Fredholm integral equations with Green's type kernel functions are solved.•Effective Galerkin methods and iterated Galerkin method are proposed for SSNFIE with Green's type kernel function.•Both the theoretical and numerical convergence of the GM and IGM for SS- NFIEs have been established.•IGM depicts superconvergence rates.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2024.128880