Numerical Algorithms

, Volume 78, Issue 2, pp 355–377 | Cite as

A new approach for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization

  • Diana Estévez Schwarz
  • René Lamour
Original Paper


This article describes a new algorithm for the computation of consistent initial values for differential-algebraic equations (DAEs). The main idea is to formulate the task as a constrained optimization problem in which, for the differentiated components, the computed consistent values are as close as possible to user-given guesses. The generalization to compute Taylor coefficients results immediately, whereas the amount of consistent coefficients will depend on the size of the derivative array and the index of the DAE. The algorithm can be realized using automatic differentiation (AD) and sequential quadratic programming (SQP). The implementation in Python using AlgoPy and SLSQP has been tested successfully for several higher index problems.


DAE Differential-algebraic equation Consistent initial value Index Derivative array Projector based analysis Nonlinear constrained optimization SQP Automatic differentiation 

Mathematics Subject Classification (2010)

65L05 65L80 34A09 34A34 65D25 90C30 90C55 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Beuth Hochschule für Technik BerlinBerlinGermany
  2. 2.Department of MathematicsHumboldt-University of BerlinBerlinGermany

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