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

Kouji Hashimoto*, Ryohei Abe, Mitsuhiro T. Nakao, Yoshitaka Watanabe

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)111-131
ページ数21
ジャーナルJapan Journal of Industrial and Applied Mathematics
22
1
出版ステータスPublished - 2005 2月
外部発表はい

ASJC Scopus subject areas

  • 工学(全般)
  • 応用数学

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