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

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

研究成果: ジャーナルへの寄稿記事

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.

元の言語英語
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
発行部数1
DOI
出版物ステータス出版済み - 2 2005

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Numerical Verification
A Priori Error Estimates
Singularly Perturbed Problem
Nonlinearity
Exponential Fitting
Nonlinear Boundary Value Problems
Finite Element Approximation
Green's function
Approximation Methods
Boundary value problems
Numerical methods
Numerical Methods
Verify
Perturbation
Numerical Examples
Term

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

これを引用

A numerical verification method for solutions of singularly perturbed problems with nonlinearity. / Hashimoto, Kouji; Abe, Ryohei; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka.

:: Japan Journal of Industrial and Applied Mathematics, 巻 22, 番号 1, 02.2005, p. 111-131.

研究成果: ジャーナルへの寄稿記事

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