Abstract
A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.
Original language | English |
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Pages (from-to) | 953-966 |
Number of pages | 14 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 223 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jan 15 2009 |
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics