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: Contribution to journalArticle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
    1
    DOI
    出版ステータス出版済み - 2 2005

    All Science Journal Classification (ASJC) codes

    • 工学(全般)
    • 応用数学

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