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FALL 2013 A sinc quadrature method for the Urysohn integral equation
K. Maleknejad, K. Nedaiasl
J. Integral Equations Applications 25(3): 407-429 (FALL 2013). DOI: 10.1216/JIE-2013-25-3-407


In this paper, we study the numerical approximation of the Urysohn integral equation with two methods. The methods are developed by means of the sinc approximation with the Single Exponential (SE) and Double Exponential (DE) transformations. These numerical methods combine a sinc Nystr\"{o}m method with the {N}ewton iterative process that involves solving a nonlinear system of equations. We provide an error analysis for the methods. These methods improve conventional results and achieve exponential convergence. Some numerical examples are given to confirm the accuracy and ease of implementation of the methods.


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K. Maleknejad. K. Nedaiasl. "A sinc quadrature method for the Urysohn integral equation." J. Integral Equations Applications 25 (3) 407 - 429, FALL 2013.


Published: FALL 2013
First available in Project Euclid: 16 December 2013

zbMATH: 1321.65192
MathSciNet: MR3161620
Digital Object Identifier: 10.1216/JIE-2013-25-3-407

Primary: 65J15 , 65R20

Keywords: Nyström method , sinc approximation , Urysohn integral equation

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

Vol.25 • No. 3 • FALL 2013
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