Numerical Solution Of Several Kinds Of Functional Integral Equations With Proportional Delay

Integral equation is an important mathematical tool in the scientific research and engineering design. Many problems can be translated into the problem of integral equation in electrostatics, electrodynamics, elastic mechanics, fluid mechanics, and other areas. Integral equation problem has a wide range of theoretical research and practical application value. Volterra type integral equation, Fredholm type integral equation and Fredholm-Volterra integral equation of mixed type are the most common of the 3 types of integral equations. Many practical problems in science can be attributed to the 3 types of equations to solve the problem. The integral equation is the emphasis and difficulty in the research of integral equations. This paper attempts to study the high accuracy numerical solution method and the theoretical analysis of the proportional integral equation with time delay.In chapter 2, Using Banach fixed point theorem, we give the proof of the Fredholm with analytic solution existence uniqueness and the Legendre collocation method, finally convergence analysis is carried out.In chapter 3, we give the proof of the existence and uniqueness of the analytic solution of the Volterra type integral equation and the relevant convergence analysis.The successive approximation solution and the optimal square approximation method are given.In chaper 4, we give the proof of the mixed Fredholm-Volterra integral equations with analytic solution existence uniqueness, and give the optimal square approximation method. We carry out the convergence analysis, and through several numerical examples of error analysis and algorithm analysis and comparison.