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

Preprint 2019-08



Diana Estévez Schwarz and René Lamour


Projected Explicit and Implicit Taylor Series Methods for DAEs. 


Abstract: The only recently developed new algorithm for computing consistent initial values and Taylor coefficients for DAEs using projector based con- strained optimization opens new possibilities to apply Taylor series integra- tion methods. In this paper, we show how corresponding projected explicit and implicit Taylor series methods can be adapted for DAEs of arbitrary index. Owing to our formulation as a projected optimization problem con- strained by the derivative array, no explicit description of the inherent dy- namics is necessary and various Taylor integration schemes can be defined straightforward. In particular, we address higher-order Pade ́ methods that stand out due to their stability and order properties. We further discuss sev- eral aspects of our prototype implemented in Python using Automatic Dif- ferentiation. The methods have been successfully tested for examples aris- ing from multibody systems simulation and a higher-index DAE benchmark arising from servo-constraint problems.



Keywords: Taylor series methods, DAE, differential-algebraic equation, con- sistent initial value, index, derivative array, projector based analysis, nonlinear constrained optimization, automatic differentiation


MSC-Classification: 65L05, 65L80, 34A09, 34A34, 65D25, 90C30, 90C55



Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2019-08


27 pp.