Aufgrund von Vorbereitungen auf eine neue Version von KOPS, können am Montag, 6.2. und Dienstag, 7.2. keine Publikationen eingereicht werden. (Due to preparations for a new version of KOPS, no publications can be submitted on Monday, Feb. 6 and Tuesday, Feb. 7.)

Runge-Kutta Discretizations of Singularly Perturbed Gradient Equations

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

BEYN, Wolf-Jürgen, Johannes SCHROPP, 2000. Runge-Kutta Discretizations of Singularly Perturbed Gradient Equations. In: BIT - Numerical Mathematics. 40(3), pp. 415-433. ISSN 0006-3835. eISSN 1572-9125. Available under: doi: 10.1023/A:1022359511479

@article{Beyn2000Runge-43181, title={Runge-Kutta Discretizations of Singularly Perturbed Gradient Equations}, year={2000}, doi={10.1023/A:1022359511479}, number={3}, volume={40}, issn={0006-3835}, journal={BIT - Numerical Mathematics}, pages={415--433}, author={Beyn, Wolf-Jürgen and Schropp, Johannes} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <bibo:uri rdf:resource=""/> <dc:creator>Schropp, Johannes</dc:creator> <dcterms:issued>2000</dcterms:issued> <dcterms:isPartOf rdf:resource=""/> <dc:creator>Beyn, Wolf-Jürgen</dc:creator> <dc:date rdf:datatype="">2018-09-06T07:31:50Z</dc:date> <dc:contributor>Schropp, Johannes</dc:contributor> <dc:language>eng</dc:language> <dc:contributor>Beyn, Wolf-Jürgen</dc:contributor> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:available rdf:datatype="">2018-09-06T07:31:50Z</dcterms:available> <dspace:isPartOfCollection rdf:resource=""/> <dcterms:title>Runge-Kutta Discretizations of Singularly Perturbed Gradient Equations</dcterms:title> <dcterms:abstract xml:lang="eng">We analyze Runge-Kutta discretizations applied to singularly perturbed gradient systems. It is shown in which sense the discrete dynamics preserve the geometric properties and the longtime behavior of the underlying ordinary differential equation. If the continuous system has an attractive invariant manifold then numerical trajectories started in some neighbourhood (the size of which is independent of the step-size and the stiffness parameter) approach an equilibrium in a nearby manifold. The proof combines invariant manifold techniques developed by Nipp and Stoffer for singularly perturbed systems with some recent results of the second author on the global behavior of discretized gradient systems. The results support the favorable behavior of ODE methods for stiff minimization problems.</dcterms:abstract> </rdf:Description> </rdf:RDF>

This item appears in the following Collection(s)

Search KOPS


My Account