서지주요정보
(A) numerical solution of abel integral equations of the second kind using continued fraction = 연분수를 이용한 아벨 적분 방정식의 수치적 해법
서명 / 저자 (A) numerical solution of abel integral equations of the second kind using continued fraction = 연분수를 이용한 아벨 적분 방정식의 수치적 해법 / Jeong-Rock Yoon.
발행사항 [대전 : 한국과학기술원, 1995].
Online Access 원문보기 원문인쇄

등록번호

8005164

소장위치/청구기호

학술문화관(문화관) 보존서고

MMA 95013

도서상태

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#### 초록정보

We consider the special case of $\alpha=\frac{1}{2}$ of Abel integral equations of the second kind. This type has much of physical applications. In many numerical attacks for this problem, we choose the method to approximate the singular kernel $(t - s)^{-\frac{1}{2}}$ with some smooth ones. This observation is quite natural and simple. Our main idea is to approximate the singular kernel $(t - s)^{-\frac{1}{2}}$ with continued fractions. The ν th step continued fraction contains (ν + 1) multiplications, whereas polynomials of degree n contains $\frac{n(n+1)}{2}$ multiplications. So if we use continued fractions instead of polynomials to approximate the singular kernel $(t - s)^{-\frac{1}{2}}$, then we gain more efficiency. We have shown that the degree of convergence is $O(\frac{1}{ν})$ which corresponds to $O(\frac{1}{n^2})$, where ν is the step of continued fractions and n is the degree of polynomials. Since the polynomial approximation yields $O(\frac{1}{n})$, we have an improvement. And many practical examples were treated.

#### 서지기타정보

청구기호 {MMA 95013 [ii], 37 p. : 삽도 ; 26 cm 영어 Includes appendix 저자명의 한글표기 : 윤정록 지도교수의 영문표기 : U-Jin Choi 지도교수의 한글표기 : 최우진 학위논문(석사) - 한국과학기술원 : 수학과, Reference : p. 35-37 Continued fractions. Volterra 방정식. --과학기술용어시소러스 연분수. --과학기술용어시소러스 Abel integral equations.
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