Superconvergence Results for Weakly Singular Fredholm-Hammerstein Integral Equations

In this article, we consider the multi-Galerkin method for solving the Fredholm-Hammerstein integral equations with weakly singular kernels, using piecewise polynomial bases. We show that multi-Galerkin method has order of convergence for the algebraic kernel, whereas for logarithmic kernel, it conv...

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Vydáno v:Numerical functional analysis and optimization Ročník 40; číslo 5; s. 548 - 570
Hlavní autoři: Mandal, Moumita, Nelakanti, Gnaneshwar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 04.04.2019
Taylor & Francis Ltd
Témata:
Algebra
Convergence
Formulas (mathematics)
Fredholm-Hammerstein integral equations
Galerkin method
Integral equations
Kernels
Mathematical analysis
multi-Galerkin method
piecewise polynomial
Polynomials
Smoothness
superconvergence rates
weakly singular kernels
ISSN:0163-0563, 1532-2467
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Shrnutí:In this article, we consider the multi-Galerkin method for solving the Fredholm-Hammerstein integral equations with weakly singular kernels, using piecewise polynomial bases. We show that multi-Galerkin method has order of convergence for the algebraic kernel, whereas for logarithmic kernel, it converges with the order in uniform norm, where h is the norm of the partition and r is the smoothness of the solution. We also discuss the iterated multi-Galerkin method. We prove that iterated multi-Galerkin method has order of convergence for the algebraic kernel and for logarithmic kernel, it has order of convergence of order in uniform norm. Numerical examples are given to illustrate the theoretical results.
Bibliografie:ObjectType-Article-1
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2018.1561468