Solution of nonlinear integral equations by Newton method

SUMMARY Solution of Nonlinear Regular integral Equations By Newton Method Ahmet BOZ Master Thesis, Department of Mathematics Thesis Supervisor : ProfDr.Binali MUSAYEV In this study, by the help of Newton Method nonlinear regular integral equations the problems of existance of solutions and its approximate solutions are being examined. The first section involves essential concepts and basic information used in the following sections. Banach Spaces, lasting linear operators, inverse operators, differential calculations of nonlinear operators, classification of integral equations, Banach Fixed Point Principle are included in these sections. In the second section, among the certain approximate solution methods of integral equations ; Iterative Method, Fredholm Determinations Method, Iterated Kernel Method and some applications of these have been given. In the third section, results about the convergence of the Newton Method which are generalized by Kantaroviç L.V. for the nonlinear equations with operator are being examined. In this section, the problem of choosing primary approache which are one of the basic phase of this method is dealt with and approximate solutions of some class nonlinear regular integral equations are found by the help of the Newton Method. Theorem 3.1.3, Theorem 3.2.2 which are proved about this subject and its applications in the problem of 3.2.8 are orijinal. Key Words : Lineer and nonlinear regular integral operators, inverse operators, Freshe derivative of nonlinear operators, resolvent kernels, Lineer and nonlinear Fredholm and Volterra integral equations.