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Stochastic DAEs in Circuit Simulation

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Modeling, Simulation, and Optimization of Integrated Circuits

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 146))

Abstract

Stochastic differential-algebraic equations (SDAEs) arise as a mathematical model for electrical network equations that are influenced by additional sources of Gaussian white noise. We sketch the underlying analytical theory for the existence and uniqueness of strong solutions, provided that the systems have noise-free constraints and are uniformly of DAE-index 1. In the main part we analyze discretization methods. Due to the differential-algebraic structure, implicit methods will be necessary. We start with a general p-th mean stability result for drift-implicit one-step methods applied to stochastic differential equations (SDEs). We discuss its application to drift-implicit Euler, trapezoidal and Milstein schemes and show how drift-implicit schemes for SDEs can be adapted to become directly applicable to stochastic DAEs. Test results of a drift-implicit Euler scheme with a mean-square step size control are presented for an oscillator circuit.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, Berlin, Germany

    Werner Römisch & Renate Winkler

Authors
  1. Werner Römisch
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  2. Renate Winkler
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Entwurfsautomatisierung, Technische Universität München, Arcisstr. 21, D-80333, München, Germany

    Kurt Antreich

  2. Zentrum Mathematik - M2, Technische Universität München, Boltzmannstr. 3, D-85748, Garching b. München, Germany

    Roland Bulirsch  & Peter Rentrop  & 

  3. Siemens AG, CT PP 2, Otto-Hahn-Ring 6, D-81730, München, Germany

    Albert Gilg

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© 2003 Springer Basel AG

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Römisch, W., Winkler, R. (2003). Stochastic DAEs in Circuit Simulation. In: Antreich, K., Bulirsch, R., Gilg, A., Rentrop, P. (eds) Modeling, Simulation, and Optimization of Integrated Circuits. ISNM International Series of Numerical Mathematics, vol 146. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8065-7_19

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  • DOI: https://doi.org/10.1007/978-3-0348-8065-7_19

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9426-5

  • Online ISBN: 978-3-0348-8065-7

  • eBook Packages: Springer Book Archive

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