Martin-Luther-Universität Halle-Wittenberg

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Manuela Bank-Zillmann

Telefon: +49 345 55-21004
Telefax: +49 345 55-27404

Universitätsplatz 8/9
06108 Halle

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Marlis Hochbruck: "On the stability of leap-frog type methods"

Termin Donnerstag, 14. Juni 2018, 17.00 - 18.15 Uhr
Veranstaltungsart Kolloquium
Reihe Interdisziplinäres Kolloquium der Naturwissenschaftlichen Fakultät II
Einrichtung Naturwissenschaftliche Fakultät II
Veranstalter Naturwissenschaftliche Fakultät II
Veranstaltungsort Weinberg Campus, Gustav-Mie-Saal
Straße Theodor-Lieser-Straße 9
PLZ/Ort 06120 Halle (Saale)
Ansprechpartner Prof. Dr. Martin Arnold
Telefon +49 345-5524653
E-Mail martin.arnold@mathematik.uni-halle.de

Beschreibung

In this talk we discuss the stability of leap-frog type methods. The standard test problem to study the stability is the unforced harmonic oscillator with a fixed frequency. It is well known that the leap-frog method is stable (in the sense that the approximation remains bounded uniformly w.r.t. the simulation time) if the product of the frequency with the time step size is strictly smaller than two. Modifications of the leap-frog method which weaken this strong step size restriction have been recently proposed in the literature. However, these schemes lose the stability property of the leap-frog method.

In this talk we present a general stability result for such time integration methods and show how to construct stable variants of the leap-frog method allowing for larger time step sizes. Numerical results show the superior stability and convergence properties of these new methods compared to recent schemes.
This is joint work with Andreas Sturm, KIT, supported by DFG CRC 1173.

Webseite https://na.math.kit.edu/marlis/

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