Title: On a nonlinear integro-differential equation of Fredholm type

Authors: Mohammed Charif Bounaya; Samir Lemita; Mourad Ghiat; Mohamed Zine Aissaoui

Addresses: Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945, Guelma, 24000, Algeria ' Départment de Sciences Exactes, Ecole Normale Supérieure, Ouargla, 30000, Algeria ' Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945, Guelma, 24000, Algeria ' Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945, Guelma, 24000, Algeria

Abstract: This work concerns an analytical and numerical study for a nonlinear Fredholm integro-differential equation, in this respect, we treat the conditions ensuring the existence and uniqueness of the solution for different varieties of kernels, thereafter, we construct a numerical approach based on the well known Nyström method. The numerical examples illustrate the efficiency of the proposed method in connection with the existence and uniqueness conditions.

Keywords: Fredholm equation; integro-differential equation; fixed point theorem; Nyström method; Newton-Côtes rules; successive approximations.

DOI: 10.1504/IJCSM.2021.10036905

International Journal of Computing Science and Mathematics, 2021 Vol.13 No.2, pp.194 - 205

Received: 08 Apr 2019
Accepted: 06 Apr 2020
Published online: 13 Apr 2021 *

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