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BIT Numerical Mathematics
Published in: BIT Numerical Mathematics 1/2017

05-10-2016

Superconvergent Nyström method for Urysohn integral equations

Authors: Chafik Allouch, Driss Sbibih, Mohamed Tahrichi

Published in: BIT Numerical Mathematics | Issue 1/2017

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Abstract

Integral equations occur naturally in many fields of mechanics and mathematical physics. In this paper a superconvergent Nyström method has been used for solving one of the most important cases in nonlinear integral equations which is called Urysohn form. Using an interpolatory projection at the set of r Gauss points, it is shown that the proposed method has an order of 3r and one step of iteration improve the convergence order to 4r. The size of the nonlinear system of equations that must be solved to calculate the approximate solution using this method remains the same as the range of the interpolatory projection. Numerical results are given to illustrate the improvement of the order.
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Metadata
Title
Superconvergent Nyström method for Urysohn integral equations
Authors
Chafik Allouch
Driss Sbibih
Mohamed Tahrichi
Publication date
05-10-2016
Publisher
Springer Netherlands
Published in
BIT Numerical Mathematics / Issue 1/2017
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-016-0629-6

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