Analytical and numerical study of nonlinear integral equations
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Date
2022-03
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Université de M'sila
Abstract
The main objective of this thesis is to offer a theoretical and numerical study on nonlinear
integral equations. We have used different fixed point theorems, and Leray-Schauder
principle to provide existence results for nonlinear integral equations on bounded
and unbounded domains, we have also presented efficient methods for solving such
equations with a thorough study on the convergence analysis. Furthermore, we have applied
some of these methods, specially, spectral collocation methods and Sinc-Nyström
methods in order to find numerical solutions of certain nonlinear integral equations,
these methods reduce the nonlinear integral equation to a system of nonlinear algebraic
equations and that algebraic system has been solved by Newton’s method. We have
derived an error analysis for the current methods, which prove that they have exponential
convergence order. Finally, several numerical examples are given to show the
effectiveness of our approaches.
Description
Keywords
Nonlinear integral equations, fixed-point theorems, Urysohn integral equation, Hammerstein integral equation half-line, projection method, Sinc-Nyström method, convergence analysis