Numerical Solution And Convergence Analysis Of Two-Dimensional Fredholm Type Functional Integral Equations

In this paper,the efficient numerical solutions including the radial basis function meshless solution,the best squares approximation solution,and the fixed point iteration and iterative acceleration algorithm are used to solve the 2-dimensional Fredholm functional integral equation.Meanwhile,the algorithm format,error estimations and convergence analysis results are obtained respectively.Moreover,the numerical examples are presented to illustrate the feasibility and reliability of the presented methods.In chapter one,the existence and uniqueness theorems and the well-posed conditions of the functional integral equation solution are given.In chapter two,the radial basis function meshless solution is introduced to solve the 2-dimensional Fredholm functional integral equation.Meanwhile,the algorithm format,error estimations and convergence analysis are obtained.Moreover,the numerical examples are presented to illustrate the feasibility and reliability of the presented method.The best square approximation method is mainly used for function approximation problems,and in this paper,the method is applied to solve the integral equation problems.In chapter three,the best squares approximation solution is introduced to solve the 2-dimensional Fredholm functional integral equation.Meanwhile,the algorithm format,error estimations and convergence analysis are obtained.Moreover,the numerical examples are presented to illustrate the feasibility and reliability of the presented method.In addition,the method proposed in this chapter and that in chapter two is compared and analyzed.The fixed point iteration and iterative acceleration algorithm are mainly used for the root finding problems of the nonlinear equations,and in this paper,the method are applied to solve the functional integral equation problems.In chapter four,the fixed point iteration,Aitken iterative acceleration algorithm and Steffensen iterative acceleration algorithm are adopted respectively to solve the 2-dimensional Fredholm functional integral equation.Meanwhile,the algorithm format,error estimations andconvergence analysis are obtained.Moreover,the numerical examples are presented to illustrate the feasibility and reliability of the presented method.