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

Yoshitaka Watanabe

doi:10.1007/BF03186533

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

Yoshitaka Watanabe

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 language	English
Pages (from-to)	233-247
Number of pages	15
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	26
Issue number	2-3
DOIs	https://doi.org/10.1007/BF03186533
Publication status	Published - Oct 2009

All Science Journal Classification (ASJC) codes

Engineering(all)
Applied Mathematics

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10.1007/BF03186533

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title = "A numerical verification method for two-coupled elliptic partial differential equations",

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.",

author = "Yoshitaka Watanabe",

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AB - 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.

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JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

IS - 2-3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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