Numerical Solution Of Fredholm Integral Equation Based On Chebyshev Neural Network

Integral equations are an important mathematical tool for scientific research and solving engineering problems.Combined with practical application of integral equations,numerical methods have become the focus.In recent years,neural network theory has developed rapidly,and its nonlinear approximation ability to function approximation research has superiority.With the continuous improvement of neural network model,the neural network based on orthogonal polynomial has more powerful approximation ability to nonlinear functions.The theory proves that the neural network performance based on Chebyshev polynomial function is optimal.Two kinds of Fredholm integral equations are studied by Chebyshev neural network.The first chapter summarizes the research background and significance of the integral equation,briefly describes the research status of the integral equation problem at home and abroad.The second chapter mainly introduces the definition and classification of the integral equation,also simply presents the mathematical model of the artificial neural network,as well as the definition and properties of Cheby-shev orthogonal basis functions,Chebyshev neural network topology,related theories,lemmas of learning algorithms,which are the basic knowledge of this paper.Chapter three applies Chebyshev neural network to solve nonlinear Fredholm integral equation.First gives the numerical approximation format,an effi-cient method based on the formalism of Chebyshev neural network is discussed.The efficiency of the mentioned approach is theoretically justified and illustrated through several numerical examples.In the fourth chapter,the Chebyshev neural network is used to solve the linear Fredholm integral equation sys-tem.Numerically discretizing the equations to obtain matrix equations,construct a reasonable Chebyshev neural network topology and give the algorithm step.the algorithm error is still theoretically analyzed,several qualitative and quantitative examples verify the feasibility of the method in this thesis.Chapter five summarizes and forecasts the work of this paper.