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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Beuth Hochschule für Technik Berlin, Luxemburger Strasse 10, 13353, Berlin, Germany

    Diana Estévez Schwarz

  2. Department of Mathematics, Humboldt-University of Berlin, 10099, Berlin, Germany

    René Lamour

Authors
  1. Diana Estévez Schwarz
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  2. René Lamour
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Correspondence to Diana Estévez Schwarz.

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Estévez Schwarz, D., Lamour, R. A new approach for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization. Numer Algor 78, 355–377 (2018). https://doi.org/10.1007/s11075-017-0379-9

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  • DOI: https://doi.org/10.1007/s11075-017-0379-9

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