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Main Title: Index preserving polynomial representation of nonlinear differential-algebraic systems
Author(s): Unger, Benjamin
Mehrmann, Volker
Type: Research Paper
Abstract: Recently in (9) a procedure was presented that allows to reformulate nonlinear ordinary differential equations in a way that all the nonlinearities become polynomial on the cost of increasing the dimension of the system. We generalize this procedure (called `polynomialization') to systems of differential-algebraic equations (DAEs). In particular, we show that if the original nonlinear DAE is regular and strangeness-free (i.e., it has differentiation index one) then this property is preserved by the polynomial representation. For systems which are not strangeness-free, i.e., where the solution depends on derivatives of the coefficients and inhomogeneities, we also show that the index is preserved for arbitrary strangeness index. However, to avoid ill-conditioning in the representation one should first perform an index reduction on the nonlinear system and then construct the polynomial representations. Although the analytical properties of the polynomial reformulation are very appealing, care has to be given to the numerical integration of the reformulated system due to additional errors. We illustrate our findings with several examples.
Subject(s): differential-algebraic equation
strangeness index
differentiation index
polynomial representation
nonlinear differential-algebraic system
index preservation
Issue Date: 17-Feb-2015
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 34A09 Implicit equations, differential-algebraic equations
65L80 Methods for differential-algebraic equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2015, 02
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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