Journal of Integral Equations and Applications

Superconvergent product integration method for Hammerstein integral equations

C. Allouch, D. Sbibih, and M. Tahrichi

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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.

Article information

Source
J. Integral Equations Applications, Volume 31, Number 1 (2019), 1-28.

Dates
First available in Project Euclid: 27 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1561601024

Digital Object Identifier
doi:10.1216/JIE-2019-31-1-1

Mathematical Reviews number (MathSciNet)
MR3974981

Zentralblatt MATH identifier
07080013

Subjects
Primary: 41A10: Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10} 45G10: Other nonlinear integral equations 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05] 65R20: Integral equations

Keywords
Hammerstein equations product integration Gauss points superconvergence

Citation

Allouch, C.; Sbibih, D.; Tahrichi, M. Superconvergent product integration method for Hammerstein integral equations. J. Integral Equations Applications 31 (2019), no. 1, 1--28. doi:10.1216/JIE-2019-31-1-1. https://projecteuclid.org/euclid.jiea/1561601024


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