Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation

Please always quote using this URN: urn:nbn:de:0297-zib-7052
  • In this work we present an approach for the sensitivity analysis of linearly-implicit differential-algebraic equation systems. Solutions for both, states and sensitivities are obtained by applying an extrapolated linearly implicit Euler discretization scheme. This approach is compared to the widely used sensitivity extensions of multi-step BDF methods by means of case studies. Especially, we point out the benefit of this method in the context of dynamic optimization using the sequential approach.

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Author:Martin Schlegel, Wolfgang Marquardt, Rainald Ehrig, Ulrich Nowak
Document Type:ZIB-Report
Tag:differential-algebraic systems; dynamic optimization; extrapolation methods; optimal control; sensitivity evaluation
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L06 Multistep, Runge-Kutta and extrapolation methods
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L80 Methods for differential-algebraic equations
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C31 Sensitivity, stability, parametric optimization
Date of first Publication:2002/11/12
Series (Serial Number):ZIB-Report (02-38)
Published in:Appeared in: Applied Numerical Mathematics 48 (2004) 83-102