2019 Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations
Claude Brezinski, Michela Redivo-Zaglia
J. Integral Equations Applications 31(1): 29-57 (2019). DOI: 10.1216/JIE-2019-31-1-29


In this paper, we want to exemplify the use of extrapolation methods (namely, Shanks transformations, the recursive algorithms for their implementation, and the freely available corresponding MATLAB software) in the solution of nonlinear Fredholm integral equations of the second kind. Extrapolations methods are well known in some domains of numerical analysis and applied mathematics, but, unfortunately, they are not frequently used in other domains. Thus, after presenting the most simple iterative method for the solution of Fredholm equations, we will show how the sequence it produces can be accelerated (under some assumptions) and also how the underlying system of nonlinear equations generated by it can be solved quite efficiently by a restarting method. Numerical examples and comparisons with other methods demonstrate the usefulness of these procedures.


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Claude Brezinski. Michela Redivo-Zaglia. "Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations." J. Integral Equations Applications 31 (1) 29 - 57, 2019. https://doi.org/10.1216/JIE-2019-31-1-29


Published: 2019
First available in Project Euclid: 27 June 2019

zbMATH: 07080014
MathSciNet: MR3974982
Digital Object Identifier: 10.1216/JIE-2019-31-1-29

Primary: 65B05 , 65B99 , 65H10 , 65R20

Keywords: acceleration techniques , integral equations , sequence transformations , Shanks transformations , solution of equations

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium


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Vol.31 • No. 1 • 2019
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