Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao, Takaaki Nishida:

A Numerical Verification of Nontrivial Solutions for the Heat Convection
Problem,

*Journal of Mathematical Fluid Mechanics*,
Vol.6, No.1 (2004) pp.1-20.

A computer assisted proof of bifurcated steady-state solutions for the
two-dimensional Rayleigh-B\'enard convection is described.
The method is based on an infinite dimensional fixed-point theorem using
a Newton-like operator. This paper also proposes a numerical verification
algorithm which generates automatically on a computer a set including the
exact nontrivial solution. All discussed numerical examples take into
account of the effects of rounding errors in the floating point computations.

March 2004

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