The parameterization method: an overview, rigorous numerics and applications скачать в хорошем качестве

The parameterization method: an overview, rigorous numerics and applications

ReCAP 2022 (Mar.13 - 18) https://www.recap.sci.waseda.ac.jp/re... Jean-Philippe Lessard (McGill University) The parameterization method: an overview, rigorous numerics and applications Abstract: In this talk, we review the fundamentals of the parameterization method, which provides a powerful way to obtain high order approximations of invariant manifolds in differential equations. The idea is first to introduce an invariance equation whose solution corresponds to the wanted parameterization, second to compute a numerical approximation of a solution of the invariance equation via power series and third to use the tools of rigorous numerics to validate the numerics. We present applications in the context of finite and infinite dimensional dynamical systems, namely ODEs, PDEs and delay equations.