Numerical solution of nonlinear integral equations

Abstract

Many problems are related to physics, engineering, biology, and other ap plied sciences, leading to modeling phenomena in the form of integral equa tions. The aim of this thesis is to study nonlinear integral equations: classifica tions, existenceanduniquenessofthesolutionusingtheBanachfixedpoint,and obtaining numerical solutions by using the successive approximations method, Nyströmmethod,projectionmethods,andspecificallyhighlightthewaveletmethod. All the methods used and examined for the numerical solution of nonlinear in tegral equations. Moreover, this method reduces the integral equations to sys tems of nonlinear algebraic equations that can be solved by Newton’s method. Wealso estimate the error bounds and convergence of the presented methods. Using Mathematica10.3software, several numerical examples are mentionedto demonstrate its effectiveness and accuracy in solving nonlinear integral equa tions, specifically the type of nonlinear quadratic integral equations. .