The Numerical Solution of the Fredholm Integral Equations of the Second Kind

Abstract

In this thesis we focus on the mathematical and numerical aspects of the Fredholm integral equation of the second kind due to their wide range of physical application such as heat conducting radiation, elasticity, potential theory and electrostatics. After the classification of these integral equations we will investigate some analytical and numerical methods for solving the Fredholm integral equation of the second kind. Such analytical methods include: the degenerate kernel methods, the Adomain decomposition method, the modified decomposition method and the method of successive approximations. The numerical methods that will be presented here are: Projection methods including collocation method and Galerkin method, Degenerate kernel approximation methods and Nystrom methods. The mathematical framework of these numerical methods together with their convergence properties will be analyzed. Some numerical examples implementing these numerical methods have been obtained for solving a Fredholm integral equation of the second kind. The numerical results show a closed agreement with the exact solution.