 The Index of an Infinite Dimensional Implicit SystemS.L. Campbell and W. Marszalek Mathematical and Computer Modelling of Dynamical Systems, 1999, vol. 5, issue 1, 18-42 Abstract: The idea of the index of a differential algebraic equation (DAE) (or implicit differential equation) has played a fundamental role in both the analysis of DAEs and the development of numerical algorithms for DAEs. DAEs frequently arise as partial discretizations of partial differential equations (PDEs). In order to relate properties of the PDE to those of the resulting DAE it is necessary to have a concept of the index of a possibly constrained PDE. Using the finite dimensional theory as motivation, this paper will examine what one appropriate analogue is for infinite dimensional systems. A general definition approach will be given motivated by the desire to consider numerical methods. Specific examples illustrating several kinds of behavior will be considered in some detail. It is seen that our definition differs from purely algebraic definitions. Numerical solutions, and simulation difficulties, can be misinterpreted if this index information is missing. Date: 1999 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:nmcmxx:v:5:y:1999:i:1:p:18-42 Ordering information: This journal article can be ordered from Access Statistics for this article Mathematical and Computer Modelling of Dynamical Systems is currently edited by I. Troch More articles in Mathematical and Computer Modelling of Dynamical Systems from Taylor & Francis Journals |
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