DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Choi, U-Jin | - |
dc.contributor.advisor | 최우진 | - |
dc.contributor.author | Yoon, Jeong-Rock | - |
dc.contributor.author | 윤정록 | - |
dc.date.accessioned | 2011-12-14T04:59:48Z | - |
dc.date.available | 2011-12-14T04:59:48Z | - |
dc.date.issued | 1995 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=98723&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/42410 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수학과, 1995.2, [ [ii], 37 p. ] | - |
dc.description.abstract | 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. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.title | (A) numerical solution of abel integral equations of the second kind using continued fraction | - |
dc.title.alternative | 연분수를 이용한 아벨 적분 방정식의 수치적 해법 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 98723/325007 | - |
dc.description.department | 한국과학기술원 : 수학과, | - |
dc.identifier.uid | 000933330 | - |
dc.contributor.localauthor | Choi, U-Jin | - |
dc.contributor.localauthor | 최우진 | - |
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