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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2016-01

Diana Estévez Schwarz and René Lamour

 

Consistent initialization for higher-index DAEs using a projector based minimum-norm specification.

 

Abstract: Higher index differential-algebraic equations (DAEs) present explicit and hidden constraints that restrict the prescription of initial values. In general, these constrains form an underdetermined system of equations, which can be solved in different ways. In this contribution we present a new method that, by construction, realizes a prescription for some differentiated components considering a special minimum-norm specification. The constraints yield adequate values for the undifferentiated components and for the remaining differentiated components. The orthogonal projectors that describe these different types of components are calculated considering the derivative array obtained by automatic differentiation.

 

Keywords: DAE, differential-algebraic equation, index derivative array, projector based analysis, consistent initial value, taylor series, automatic differentiation, underdetermined systems of equations

 

MSC-Classification: 65L05, 65L80, 34A34, 65D25, 41A58

 

 

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2016-01

 

30 pp.