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Superconvergence Results for Weakly Singular Fredholm–Hammerstein Integral Equations
, G. Nelakanti
Published in Taylor and Francis Inc.
Volume: 40
Issue: 5
Pages: 548 - 570
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 O(h r+α ) for the algebraic kernel, whereas for logarithmic kernel, it converges with the order O(log h h r+1 ) 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 O(h r+2α ) for the algebraic kernel and for logarithmic kernel, it has order of convergence of order O((log h) 2 h r+2 ) in uniform norm. Numerical examples are given to illustrate the theoretical results. © 2018, © 2019 Taylor & Francis Group, LLC.
About the journal
JournalData powered by TypesetNumerical Functional Analysis and Optimization
PublisherData powered by TypesetTaylor and Francis Inc.