Méthodes Computationnelles pour la Résolution des Équations Intégrales Non Linéaires
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Date
2017-06-29
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Université de M'sila
Abstract
Many problems which arise in mathematical physics, engineering, biology,
economics,…etc., lead to mathematical models described by nonlinear integral
equations. The aim of this research is to find the solution of nonlinear Volterra
and Fredholm integral equation by using analytical and numerical methods
such as the degenerate kernel method, the successive approximation method,
the projection method, and the Nyström method. Also, we applied the new
combination of Newton-Kantorovich method with modified Simpson method.
Most of them transform the nonlinear integral equation into a system of linear
or nonlinear algebraic equations. Finally, numerical examples are presented
which demonstrate the robustness of the expansion numerical methods in
determining solutions.
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Keywords
Nonlinear integral equations, fixed point problem, degenerate kernel method, successive approximation method, projection method, Nyström method, Newton-Kantorovich method