論文

基本情報

氏名 橋本 弘治
氏名(カナ) ハシモト コウジ
氏名(英語) HASHIMOTO KOJI
所属 短期大学部 幼児保育学科
職名 准教授

題名

A numerical verification method for solutions of singularly perturbed problems with nonlinearity

単著・共著の別

 

著者

K Hashimoto
R Abe
MT Nakao
Y Watanabe

担当区分

 

概要

In order to verify the solutions of nonlinear boundary value problems by Nakao's computer-assisted numerical method, it is required to find a constant, as sharp as possible, in the a priori error estimates for the finite element approximation of some simple linear problems. For singularly perturbed problems, however, generally it is known that the perturbation term produces a bad effect on the a priori error estimates, i.e., leads to a large constant, if we use the usual approximation methods. In this paper, we propose some verification algorithms for solutions of singularly perturbed problems with nonlinearity by using the constant obtained in the a priori error estimates based on the exponential fitting method with Green's function. Some numerical examples which confirm us the effectiveness of our method are presented.

発表雑誌等の名称

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS

出版者

KINOKUNIYA CO LTD

22

1

開始ページ

111

終了ページ

131

発行又は発表の年月

2005-02

査読の有無

有り

招待の有無

無し

記述言語

英語

掲載種別

研究論文(学術雑誌)

国際・国内誌

 

国際共著

 

ISSN

 

eISSN

 

DOI

10.1007/BF03167479

Cinii Articles ID

 

Cinii Books ID

 

Pubmed ID

 

PubMed Central 記事ID

 

形式

無償ダウンロード

JGlobalID

 

arXiv ID

 

ORCIDのPut Code

 

DBLP ID