An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid

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    1 Citation (Scopus)

    Abstract

    Some computer-assisted proofs of nontrivial steady-state solutions for the Kolmogorov flows are presented. The method is based on the infinite-dimensional fixed-point theorem using a Newton-like operator with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial solution. When discussing the numerical results, we consider the effects of rounding errors in the floating point computations. This is a continuation of our study that was presented in Watanabe (2009).

    Original languageEnglish
    Pages (from-to)157-170
    Number of pages14
    JournalJournal of Computational and Applied Mathematics
    Volume302
    DOIs
    Publication statusPublished - Aug 15 2016

    All Science Journal Classification (ASJC) codes

    • Computational Mathematics
    • Applied Mathematics

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