A flow-on-manifold formulation of differential-algebraic-equations

dc.contributor.authorBaum, Ann-Kristin
dc.date.accessioned2021-12-17T10:11:57Z
dc.date.available2021-12-17T10:11:57Z
dc.date.issued2014-11-25
dc.description.abstractWe derive a flow formulation of differential-algebraic equations (DAEs), implicit differen-tial equations whose dynamics are restricted by algebraic constraints. Using the framework ofderivatives arrays and the strangeness-index, we identify the systems that are uniquely solv-able on a particular set of initial values and thus possess a flow, the mapping that uniquelyrelates a given initial value with the solution through this point. The flow allows to studysystem properties like invariant sets, stability, monotonicity or positivity. For DAEs, theflow further provides insights into the manifold onto which the system is bound to and intothe dynamics on this manifold. Using a projection approach to decouple the differential andalgebraic components, we give an explicit representation of the flow that is stated in theoriginal coordinate space. This concept allows to study DAEs whose dynamics are restrictedto special subsets in the variable space, like a cone or the nonnegative orthant.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15799
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14572
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherdifferential-algebraic equationsen
dc.subject.otherflowen
dc.subject.otherflow on surfaceen
dc.subject.otherdynamical systemsen
dc.titleA flow-on-manifold formulation of differential-algebraic-equationsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2014, 37en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200034A09 Implicit equations, differential-algebraic equationsen
tub.subject.msc200037C10 Vector fields, flows, ordinary differential equationsen

Files

Original bundle
Now showing 1 - 1 of 1
Loading…
Thumbnail Image
Name:
Preprint-37-2014.pdf
Size:
571.39 KB
Format:
Adobe Portable Document Format

Collections