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2019 Superconvergent product integration method for Hammerstein integral equations
C. Allouch, D. Sbibih, M. Tahrichi
J. Integral Equations Applications 31(1): 1-28 (2019). DOI: 10.1216/JIE-2019-31-1-1

Abstract

In this paper, we define a superconvergent projection method for approximating the solution of Hammerstein integral equations of the second kind. The projection is chosen either to be the orthogonal or an interpolatory projection at Gauss points onto the space of discontinuous piecewise polynomials. For a smooth kernel or one less smooth along the diagonal, the order of convergence of the proposed method improves upon the classical product integration method. Several numerical examples are given to demonstrate the effectiveness of the current method.

Citation

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C. Allouch. D. Sbibih. M. Tahrichi. "Superconvergent product integration method for Hammerstein integral equations." J. Integral Equations Applications 31 (1) 1 - 28, 2019. https://doi.org/10.1216/JIE-2019-31-1-1

Information

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

zbMATH: 07080013
MathSciNet: MR3974981
Digital Object Identifier: 10.1216/JIE-2019-31-1-1

Subjects:
Primary: 41A10, 45G10, 47H30, 65R20

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.31 • No. 1 • 2019
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