HAMANI, Fatima2022-07-042022-07-042022-03http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/29971The 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.Nonlinear integral equations, fixed-point theorems, Urysohn integral equation, Hammerstein integral equation half-line, projection method, Sinc-Nyström method, convergence analysisThesis