A numerical verification of nontrivial solutions for the heat convection problem (Q1430499)

The authors study two-dimensional Rayleigh-Bénard convection in Oberbeck-Boussinesq approximation. The solution is represented in double Fourier series, and then an infinite-dimen\-sional fixed-point formulation is introduced. The solution is constructed by iteration using a Newton-like operator and some a priori error estimates obtained for linearized problems. This paper also proposes a computer verification algorithm which generates automatically a set including the exact nontrivial solution. The method is illustrated by computing the first and second bifurcated solutions from the trivial solution. Numerical examples take into account rounding errors in the floating point computations.