Analytical and numerical approach for a nonlinear Volterra-Fredholm integro-differential equation

Mohammed Charif Bounaya; Samir Lemita; Sami  Touati; Mohamed Zine  Aissaoui

doi:10.5269/bspm.52191

Mohammed Charif Bounaya Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945, Guelma, Algerie. https://orcid.org/0000-0001-7969-8031
Samir Lemita école normale supérieure Ouergla
Sami Touati Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945, Guelma, Algerie. https://orcid.org/0000-0002-4946-4805
Mohamed Zine Aissaoui Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945, Guelma, Algerie. https://orcid.org/0000-0001-5253-9671

Abstract

An approach for Volterra- Fredholm integro-differential equations using appropriate fixed point theorems of existence, uniqueness is presented. The approximation of the solution is performed using Nystrom method in conjunction with successive approximations algorithm. Finally, we give a numerical example, in order to verify the effectiveness of the proposed method with respect to the analytical study.

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