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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Rigorous Numerics Using Conley Index Theory

Rigorous Numerics Using Conley Index Theory

Miller, Ulrich

Paperback

Series: Augsburger Schriften Zur Mathematik, Physik Und Informatik, Book 9

General Computers

Currently unavailable to order

ISBN10: 3832508546
ISBN13: 9783832508548
Publisher: Logos Verlag Berlin
Published: Mar 15 2005
Pages: 121
Weight: 0.39
Height: 0.40 Width: 5.70 Depth: 8.00
Language: English
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.

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