Iteration Correction Method For Two Dimensional Fredholm Integral Equations Of The Second Kind

In electrostatics, electrodynamics, elastic mechanics, fluid mechanics, electromagnetic theory, radiation science, Earth exploration and other subjects, many problems can be transformed into solving the corresponding integral equations. Ordinary differential equations and partial differential equations can be transformed into the equivalent integral equations. Some mathematical problems of the diffusion and migration phenomenon can not be solved by differential equations. So, we have to solve these problems by integral equations.This dissertation consists of three chapters. In chapter 1, we briefly introduce the definition and classification of the integral equations and summarise the known analytical methods and numerical methods for solving the integral equations and briefly introduce the two dimensional Fredholm integral equations of the second kind. Chapter 2 includes two interpolation methods and a spline integral scheme of 8 nodes based on the 8-node quadrilateral finite element. The interpolation methods are MQ RBF Interpolation and spline interpolation of 8 nodes based on the quadrilateral finite element. In chapter 3, a collocation method and an iterative correction method are used to solve two dimensional Fredholm integral equations of the second kind. The convergence of the iterative correction method is proved and the error bounds are derived. Some numerical examples are given to illustrate the efficiency of the methods and demonstrate that our methods have fast convergence and high accuracy.