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

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

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)111-131
    Number of pages21
    JournalJapan Journal of Industrial and Applied Mathematics
    Volume22
    Issue number1
    DOIs
    Publication statusPublished - Feb 2005

    All Science Journal Classification (ASJC) codes

    • Engineering(all)
    • Applied Mathematics

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