Aufgrund von Vorbereitungen auf eine neue Version von KOPS, können kommenden Montag und Dienstag keine Publikationen eingereicht werden. (Due to preparations for a new version of KOPS, no publications can be submitted next Monday and Tuesday.)
Type of Publication: | Journal article |
Publication status: | Published |
Author: | Kloeden, Peter E.; Schropp, Johannes |
Year of publication: | 2003 |
Published in: | BIT - Numerical Mathematics ; 43 (2003), 3. - pp. 571-586. - ISSN 0006-3835. - eISSN 1572-9125 |
DOI (citable link): | https://dx.doi.org/10.1023/B:BITN.0000007059.99601.18 |
Summary: |
Classes of Runge–Kutta methods preserving the monotonicity of ordinary and delay differential equations are identified. Essentially, the vector b and the matrix A from the Butcher tableau should be such that all components of b are positive and all components of the matrix B(r)A, where B(r) is the inverse of the matrix I+rA, are nonnegative for sufficiently small positive r. The latter is satisfied by all explicit, diagonally-implicit and fully implicit Runge–Kutta methods for which all of the components of the matrix A, except those that are zero by definition, are positive.
|
Subject (DDC): | 510 Mathematics |
Keywords: | monotone dynamical systems, delay equations, Runge–Kutta methods |
Bibliography of Konstanz: | Yes |
Refereed: | Unknown |
Files | Size | Format | View |
---|---|---|---|
There are no files associated with this item. |
KLOEDEN, Peter E., Johannes SCHROPP, 2003. Runge–Kutta Methods for Monotone Differential and Delay Equations. In: BIT - Numerical Mathematics. 43(3), pp. 571-586. ISSN 0006-3835. eISSN 1572-9125. Available under: doi: 10.1023/B:BITN.0000007059.99601.18
@article{Kloeden2003-09Runge-43197, title={Runge–Kutta Methods for Monotone Differential and Delay Equations}, year={2003}, doi={10.1023/B:BITN.0000007059.99601.18}, number={3}, volume={43}, issn={0006-3835}, journal={BIT - Numerical Mathematics}, pages={571--586}, author={Kloeden, Peter E. and Schropp, Johannes} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/43197"> <dc:contributor>Schropp, Johannes</dc:contributor> <dcterms:abstract xml:lang="eng">Classes of Runge–Kutta methods preserving the monotonicity of ordinary and delay differential equations are identified. Essentially, the vector b and the matrix A from the Butcher tableau should be such that all components of b are positive and all components of the matrix B(r)A, where B(r) is the inverse of the matrix I+rA, are nonnegative for sufficiently small positive r. The latter is satisfied by all explicit, diagonally-implicit and fully implicit Runge–Kutta methods for which all of the components of the matrix A, except those that are zero by definition, are positive.</dcterms:abstract> <dcterms:issued>2003-09</dcterms:issued> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:contributor>Kloeden, Peter E.</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:creator>Schropp, Johannes</dc:creator> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-09-07T09:30:02Z</dcterms:available> <dc:creator>Kloeden, Peter E.</dc:creator> <dcterms:title>Runge–Kutta Methods for Monotone Differential and Delay Equations</dcterms:title> <dc:language>eng</dc:language> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-09-07T09:30:02Z</dc:date> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/43197"/> </rdf:Description> </rdf:RDF>