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The Study of Numerical Algorithms for a Class of Hypersingular Integral Equation

Author: ZhaoSuoSuo
Tutor: ChenYiMing；LiJin
School: Yanshan University
Course: Computational Mathematics
Keywords: Hadmard Credits Interpolation function Numerical Approximation Strongly Singular Integral Cauchy integral
CLC: O241.83
Type: Master's thesis
Year: 2010
Downloads: 64
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Abstract


Strongly singular integral equations numerical algorithms developed in recent years a new topic . It is still relatively small , but this method is demonstrated from the outset of its unique advantages and strong vitality . In this paper is to study a class of strongly singular integral equations numerical algorithms , is the solution of singular integral boundary element method to solve the difficulties , the basic idea is the use of interpolation and function approximation, given by us to strongly singular weakly singular integral conversion method , and finally the use of the Cauchy integral numerical solution to reduce the amount of computation of the strongly singular integral equations , to improve the accuracy . The estimated error of the numerical solution was further analyzed . And through numerical examples show the feasibility and effectiveness of the numerical methods . First, we briefly review the history and development of the boundary element method , contact and strong singular integral of Cauchy type singular integrals with strongly singular integral solution given research significance . Second , we give theoretical knowledge required by the papers , the first the strongly singular segment Points , strongly singular Cauchy singular integral relationship described Finally, this article Lagrange interpolation polynomial and Chebyshev orthogonal polynomials nature . Then, through numerical approximation and interpolation functions , discussed two numerical solution of the strong singular integral equation : (1) Chebyshev polynomial function approximation is proposed strong alpha order singular integral numerical algorithm , and then given two strongly singular integral to the conversion of the Cauchy singular integral theorem , the two theorems , given alpha = 2 , strong singular integrals numerically solving formula . (2 ) by singular integral theorem of Cauchy singular integral conversion , strong singular integral solving conversion of any order to solve the Cauchy singular integral using Lagrange interpolation method , given the strong second-order singular integral equations Numerical algorithm, and then gives the steps of arbitrary order strongly singular integral equation . Finally , a numerical example , fully shows that the method is effective to improve the strongly singular equation numerical methods , indicating the feasibility and effectiveness of the method .

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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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