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Several types of Volterra Integral Equations spectral collocation solution and convergence analysis
Author: ChenShaoJun
Tutor: WangQiSheng
School: Wuyi University
Course: Applied Mathematics
Keywords: Volterra integral equation FredholmVolterra integral equation Legendre spectral collocation method Chebyshev spectral collocation method Convergence analysis
CLC: O241.83
Type: Master's thesis
Year: 2011
Downloads: 55
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Abstract
In this paper, the spectral collocation methods are systematically studied for twodimensional Volterra integral equations with smooth kernel and FredholmVolterra type integral equations.Firstly, the Legendre spectral collocation method and Chebyshev spectral collocation method are proposed to solve the twodimensional 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 FredholmVolterra 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 equation are introduced, and some preliminary knowledge are given.In chapterⅡ, the methods of the numerical solution for the onedimensional 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 respectively to solve the twodimensional Volterra integral equations and the convergence analysis results are obtained.In chapterⅣ, the Legendre spectral collocation method is introduced to solve the FredholmVolterra integral equation and the convergence analysis result is given.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Integral Equation
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