View : 59 Download: 0

Numerical solutions of S.I.E. using Lobatto-Chebyshev quadrature and overdetermined systems

Title
Numerical solutions of S.I.E. using Lobatto-Chebyshev quadrature and overdetermined systems
Authors
전지현
Issue Date
1997
Department/Major
대학원 수학과
Keywords
Numerical solutionLobatto Chebyshevquadratureoverdetermined
Publisher
The Graduate School, Ewha Womans University
Degree
Master
Abstract
Many problems of mathematical physics are reducible to singular integral equations with Cauchy-type kernels. Of concern here are the Lobatto-Chebyshev formulae for the numerical solutions of singular integral equations of the Cauchy-type. Lobatto-Chebyshev quadrature at the extrema and the zeros of T_(n)(x) leads to an overdetermined system of linear algebraic equations. The coefficient matrix of the linear system of algebraic equations is shown to have an inverse, which is expressed in a neat, closed form. We show that the use of the zeros of T_(2n) as collocation yields well-conditioned coefficient matrix and good approximation to the exact solutions.;수학 물리학의 많은 문제들은 Cauchy 타입의 kernel을 가진 특이적분방정식으로 귀착된다. Cauchy타입의 특이적분방정식의 수치적 해를 구하기 위해서 Lobatto-Chebyshev 공식을 생각해 보기로 한다. T_(n)(x)의 극점들과 근들을 사용한 Lobatto-Chebyshev quadrature를 통해서 선형방정식들의 overdetermined 시스템이 얻어진다. 방정식의 선형시스템으로 이루어진 계수행렬은 잘 정리된 형태의 역행렬을 가진다. T_(2n)(x)의 근들을 collocation으로 사용할때 well- conditioned 계수행렬을 통해 정확한 해에 대한 좋은 근사 값을 가진다.
Fulltext
Show the fulltext
Appears in Collections:
일반대학원 > 수학과 > Theses_Master
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE