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A Survey on Numerical Methods for the Simulation of Initial Value Problems with sDAEs

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Surveys in Differential-Algebraic Equations IV

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

Abstract

This paper provides an overview on numerical aspects in the simulation of differential-algebraic equations (DAEs). Amongst others we discuss the basic construction principles of frequently used discretization schemes, such as BDF methods, Runge–Kutta methods, and ROW methods, as well as their adaption to DAEs. Moreover, topics like consistent initialization, stabilization, parametric sensitivity analysis, co-simulation techniques, aspects of real-time simulation, and contact problems are covered. Finally, some illustrative numerical examples are presented.

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  1. Department Mathematical Methods in Dynamics and Durability MDF, Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany

    Michael Burger

  2. Department of Aerospace Engineering, Institute of Mathematics and Applied Computing, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Matthias Gerdts

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    Achim Ilchmann

  2. Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

    Timo Reis

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Burger, M., Gerdts, M. (2017). A Survey on Numerical Methods for the Simulation of Initial Value Problems with sDAEs. In: Ilchmann, A., Reis, T. (eds) Surveys in Differential-Algebraic Equations IV. Differential-Algebraic Equations Forum. Springer, Cham. https://doi.org/10.1007/978-3-319-46618-7_5

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