Legendre superconvergent degenerate kernel and Nyström methods for nonlinear integral equations-Reference-Cited by-同舟云学术

Legendre superconvergent degenerate kernel and Nyström methods for nonlinear integral equations

Published:2023-05-24 Issue:5 Volume:75 Page:579-595
ISSN:1027-3190
Container-title:Ukrains’kyi Matematychnyi Zhurnal
language:
Short-container-title:Ukr. Mat. Zhurn.

Author:

Allouch C.,Arrai M.,Bouda H.,Tahrichi M.

Abstract

UDC 517.9 We study polynomially based superconvergent collocation methods for the approximation of solutions of nonlinear integral equations. The superconvergent degenerate kernel method is chosen for approximating the solutions of Hammerstein equations, while a superconvergent Nystr\"om method is used for solving Urysohn equations. By applying interpolatory projections based on Legendre polynomials of degree ≤ n , we analyze the superconvergence of these methods and their iterated versions. Numerical results are presented to validate the theoretical results.

Publisher

SIGMA (Symmetry, Integrability and Geometry: Methods and Application)

Subject

General Earth and Planetary Sciences,General Engineering,General Environmental Science

Reference16 articles.

1. C. Allouch, D. Sbibih, M. Tahrichi, Superconvergent product integration method for Hammerstein integral equations, J. Integral Equations and Appl., 31, 1–28 (2019).

2. C. Allouch, D. Sbibih, M. Tahrichi, Superconvergent Nyström method for Urysohn integral equations, BIT Numer. Math., 57, 3–20 (2017).

3. C. Allouch, D. Sbibih, M. Tahrichi, Superconvergent Nyström and degenerate kernel methods for Hammerstein integral equations, J. Comput. and Appl. Math., 258, 30–41 (2014).

4. C. Allouch, D. Sbibih, M. Tahrichi, Legendre superconvergent Galerkin-collocation type methods for Hammerstein equations, J. Comput. and Appl. Math., 353, 253–264 (2019).

5. K. E. Atkinson, A survey of numerical methods for solving nonlinear integral equations, J. Integral Equations and Appl., 4, 15–46 (1992).