DOI: https://doi.org/10.26089/NumMet.v23r422

Construction of the generalized iterative methods used for solution of the Fredholm integral equation

Authors

  • Sarra Boukansous
  • Xie Mande
  • Boutheina Tair
  • Hamza Guebbai

Keywords:

Fredholm integral equations
numerical integration
iterative methods

Abstract

In this paper, we consider the Fredholm integral equations of the second kind and construct a new iterative scheme associated to the Nyström method, which was elaborated by Atkinson to approximate the solution over a large interval. Primarily, we demonstrate the inability to generalize the Atkinson iterative methods. Then, we describe our modified generalization in detail and discuss its advantages such as convergence of the iterative solution to the exact solution in the sense norm of the Banach space С0[a,b]. Finally, we give a numerical examples to illustrate the accuracy and reliability of our generalization.

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Published

2022-12-07

Issue

Vol. 23 (2022): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Sarra Boukansous

Zhejiang Gongshang University,
School of Computer Science and Information Engineering
P.R, 310018, Zhejiang, China
• PhD 

Xie Mande

Zhejiang Gongshang University,
School of Computer Science and Information Engineering
P.R, 310018, Zhejiang, China
• Professor

Boutheina Tair

University 08 mai 1945,
Department of Mathematics, Laboratory of Applied Mathematics and Modeling
P. 401, 24000, Guelma, Algeria
• Leading Researcher

Hamza Guebbai

University 08 mai 1945,
Department of Mathematics, Laboratory of Applied Mathematics and Modeling
P. 401, 24000, Guelma, Algeria
• Leading Researcher

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Copyright (c) 2022 Сарpа Букансус, Се Мандэ, Бутейна Таир, Хамза Гибби

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