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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