Name: Rigorous Numerics Using Conley Index Theory (en Inglés)
Price: 98.85 USD
Availability: InStock
Author: Miller, Ulrich
ISBN: 9783832508548

portada Rigorous Numerics Using Conley Index Theory (en Inglés)

Rigorous Numerics Using Conley Index Theory (en Inglés)

Formato

Libro Físico

Editorial

Logos Verlag Berlin

Autor

Miller, Ulrich

Idioma

Inglés

N° páginas

121

Encuadernación

Tapa Blanda

ISBN13

9783832508548

Rigorous Numerics Using Conley Index Theory (en Inglés)

Miller, Ulrich (Autor) · Logos Verlag Berlin · Tapa Blanda

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Reseña del libro "Rigorous Numerics Using Conley Index Theory (en Inglés)"

Conley index theory as a tool to qualitatively study dynamical systems has been around already for several decades. In recent years more and more applications emerge concerning stable numerical computations. The Conley index is predestined for those applications since it is robust against perturbations. The rigorous numerics method presented in this book is one of these new applications and goes back to an idea of K. Mischaikow and P. Zgliczy 'nski. It allows to determine steady states of a dynamical system given as a partial differential equation (PDE). The method is called rigorous since the calculation does not only give approximations but also implies existence (and sometimes even uniqueness) of these steady states within a small box neighborhood delivered by the algorithm. In this book this method is generalized to PDE with two-dimensional domains and combined with a path-following algorithm in order to rigorously calculate branches of equilibria of parameter dependent equations. All numerical computations are given within the Cahn-Hilliard equation, but the general method and in particular the necessary estimates for cubical nonlinearities generalizes easily to other PDE.