Types Of Volterra Integral Equations Spectrum Configuration Solution And Convergence Analysis

In this paper, the spectral collocation methods are systematically studied for two-dimensional Volterra integral equations with smooth kernel and Fredholm-Volterra type integral equations.Firstly, the Legendre spectral collocation method and Chebyshev spectral collocation method are proposed to solve the two-dimensional Volterra integral equation. Secondly, we will provide a rigorous convergence analysis which theoretically justifies the spectral rate of the convergence of the proposed method. Finally, the Legendre spectral collocation method is introduced to solve the Fredholm-Volterra integral equation, and the convergence analysis results are given.This paper is organized as follows:In chapterⅠ, the research background of the spectral methods and Volterra integral equa-tion are introduced, and some preliminary knowledge are given.In chapterⅡ, the methods of the numerical solution for the one-dimensional Volterra integral equations are summarized and the main results of this paper are introduced.In chapterⅢ, the Legendre and Chebyshev spectral collocation methods are proposed re-spectively to solve the two-dimensional Volterra integral equations and the convergence analysis results are obtained.In chapterⅣ, the Legendre spectral collocation method is introduced to solve the Fredholm-Volterra integral equation and the convergence analysis result is given.