Some Results On The Discrete Legendre Multi-projection Method For Integral Equation Of The Second Kind

This thesis mainly studies that the discrete Legendre multi-projection method for solving Fredholm integral equations of the second kind with the corresponding eigen-value problem,the discrete Legendre M-Galerkin and M-Collocation methods are given.and the wavelet two-grid methods for the eigenvalue problem are studied.The paper is divided into five chapters:In Chapter 2,we give some important preliminary knowledge of this paper.We introduce some theories of the eigenvalues of integral operators,the related properties of Legendre functions,and the structure and properties of wavelet basis.In chapter 3,we focus on the discrete Legendre M-Galerkin method for Fred-holm integral equations of the second kind with the corresponding eigenvalue prob-lem.Firstly,we give the framework of the discrete Legendre multi-projection method.Then we discuss for Fredholm integral equations of the second kind and eigenvalue problem.In chapter 4,we discuss the discrete Legendre M-Collocation method for Fred-holm integral equations of the second kind with the corresponding eigenvalue prob-lem.First,the discrete Legendre M-Collocation method for Fredholm integral equa-tions of the second kind is introduced.The discrete Legendre M-Collocation method for the eigenvalue problem is given.Finally,a numerical example is given.In Chapter 5,the wavelet two-grid method is used to solve the eigenvalue problem of the integral operator for the two-grid method and the wavelet basis.Firstly,the theoretical framework of the two-grid method is introduced,and its error is analyzed theoretically.Then the wavelet basis is used in the two-grid method to solve the eigenvalue problem of the integral operator.