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

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All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

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