Numerical Solutions Of Several Nonlinear Functional Integral Equations

The numerical solution of integral equations is one of the important research topics in modern mathematics,and it is also the hot direction of theoretical research and scientific en-gineering calculation.In this paper,we mainly study the efficient numerical solutions of three types nonlinear functional integral equations,including Fredholm type and mixed type Ham-merstein functional integral equations,and Volterra type P-power functional integral equations.Firstly,the existence and uniqueness conditions of these three functional integral equations are presented;Secondly,the Algorithm format of the corresponding numerical solution method and the results of error estimation and convergence analysis are given;Finally,Matlab numerical ex-periments are given to verify the theoretical research conclusions.The specific framework is as follows:In the first chapter,the introduction part briefly introduces significance and status of the research,and the classification of functional integral equations.In the second chapter,a class of Fredholm-type Hammerstein functional integral equations is solved by Fixed point iteration and Aitkin accelerated iterative method and the results of error estimation and convergence analysis in the sense of L~?-norm are obtained.In the third chapter,using the Block Pulse basis function collocation method,a kind of mixed Hammerstein functional integral equations is solved and the error estimation and conver-gence analysis in the sense of L~2-norm are also obtained.In the fourth chapter,Galerkin projection method is used to solve the Volterra type P-power integral equation,not only the relation between the Galerkin projection method and the best square approximation method is studied but also the convergence analysis results are given.In the fifth chapter,the article reviews and prospects,and discusses some issues for further study.