A Numerical Verification Method for Two-Coupled Elliptic Partial Differential Equations
Yoshitaka Watanabe
Source: Japan J. Indust. Appl. Math. Volume 26, Number 2-3
(2009), 233-247.
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.
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Japan Journal of Industrial and Applied Mathematics
