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Manually assigned DDC number: 51256

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Title: Global, rigorous and realistic bounds for the solution of dissipative differential equations. Part I: Theory

Author:

Subject: Arnold Neumaier Global, rigorous and realistic bounds for the solution of dissipative differential equations. Part I: Theory

Description: . It is shown how interval analysis can be used to calculate rigorously valid enclosures of solutions to initial value problems for ordinary differential equations. In contrast to previously known methods, the enclosures obtained are valid over larger time intervals, and for uniformly dissipative systems even globally. This paper discusses the underlying theory; main tools are logarithmic norms and differential inequalities. Numerical results will be given in a subsequent paper. Zusammenfassung. Es wird gezeigt, wie man mit Hilfe von IntervallAnalysis rigorose Einschließungen von Losungen von Anfangswertproblemen bei gewohnlichen Differentialgleichungen berechnen kann. Im Gegensatz zu anderen Methoden sind die Einschließungen uber großere Zeitintervalle, und fur gleichmaßig dissipative Systeme sogar global gultig. Diese Arbeit behandelt die zugrundeliegende Theorie; Hauptwerkzeuge sind logarithmische Normen und Differentialungleichungen. Numerische Ergebnisse werden in einer spateren A...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1999-02-03

Pubyear: 1993

Format: ps

Identifier: http://citeseer.ist.psu.edu/140920.html

Source: http://solon.cma.univie.ac.at/~neum/ms/ode.ps.gz

Language: en

Rights: unrestricted