抄録
In this paper, we consider a numerical technique to verify the exact eigenvalues and eigenfunctions of second-order elliptic operators in some neighborhood of their approximations. This technique is based on Nakao's method [9] using the Newton-like operator and the error estimates for the C0 finite element solution. We construct, in computer, a set containing solutions which satisfies the hypothesis of Schauder's fixed point theorem for compact map on a certain Sobolev space. Moreover, we propose a method to verify the eigenvalue which has the smallest absolute value. A numerical example is presented.
本文言語 | English |
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ページ(範囲) | 307-320 |
ページ数 | 14 |
ジャーナル | Japan Journal of Industrial and Applied Mathematics |
巻 | 16 |
号 | 3 |
出版ステータス | Published - 1999 10 |
外部発表 | はい |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics