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A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem |
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| Authors: | |
| Institution: | (1) Computing and Communications Center, Kyushu University, 812-8581 Fukuoka, Japan;(2) Department of Computer Science and Information Mathematics, The University of Electro-Communications, 182-8585 Chofu, Japan;(3) Graduate School of Mathematics, Kyushu University, 812-8581 Fukuoka, Japan;(4) Graduate School of Science, Kyoto University, 606-8502 Kyoto, Japan |
| Abstract: | A computer assisted proof of the existence of nontrivial steady-state solutions for the two-dimensional Rayleigh-Bénard 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. |
| Keywords: | 35Q35 65N15 76D03 |
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