Two-Grid Iterative Method For Fredholm Integral Equation Based On Nystr?m Interpolation

In this master paper,we mainly discuss a new two-grid iterative method based on Nystrom interpolation,which is used for numerical solution of Fredholm integral equations with multi-functional factors,system of Fredholm integral equations and system of Fredholm-Hammerstein integral equations respectively,and analyze the convergence with high accuracy.As an introduction,the first part summarizes the research background and significance of this paper as well as the research status at home and abroad.The classifications of integral equation are preliminarily discussed,and the main results of this paper are given.In Chapter 2,a class of Fredholm integral equations with multi-functional factors are dis-cussed.Firstly,Nystrom interpolation is used for numerical solution on the coarse grid.Sec-ondly,we use the two-grid algorithm to get the fine grid approximation solution.Finally,a fixed point iterative scheme is constructed to obtain high precision iterative solution on the fine grid.The algorithm format,error estimation and convergence analysis are given at the same time.In Chapter 3 and Chapter 4,a class of system of Fredholm integral equations and system of Fredholm-Hammerstein integral equations are studied,respectively.The algorithm format of coarse and fine two-layer grids,the fixed point iteration format,error estimation and con-vergence analysis of the two equations under the two-grid iterative method based on Nystrom interpolation are given.The existence and uniqueness of analytical solutions of above three Fredholm type integral equations are theoretically proven by Banach fixed point theorem.In each chapter,two numer-ical examples are used to verify the effectiveness and feasibility of theoretical analysis.At the end of the paper,a summary and analysis are made.This study not only enriches the high pre-cision numerical solution of Fredholm type integral equation,but also extends the application value of Nystrom method,two-grid iterative method and fixed point iterative method.