A numerical verification method for two-coupled elliptic partial differential equations

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    Abstract

    A numerical verification method of steady state solutions for a system of reaction-diffusion equations is described. Using a decoupling technique, the system is reduced to a single nonlinear equation and a computer-assisted method for second-order elliptic boundary value problems based on the infinite dimensional fixed-point theorem can be applied. Some numerical examples confirm the effectiveness of the method.

    Original languageEnglish
    Pages (from-to)233-247
    Number of pages15
    JournalJapan Journal of Industrial and Applied Mathematics
    Volume26
    Issue number2-3
    DOIs
    Publication statusPublished - Jan 1 2009

    All Science Journal Classification (ASJC) codes

    • Engineering(all)
    • Applied Mathematics

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