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A Simple Method for Quasilinearity Analysis of DAEs

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Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 117))

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Abstract

We present a simple method for quasilinearity (QL) analysis of differential-algebraic equations (DAEs). It uses the signature matrix and offsets computed by Pryce’s structural analysis and determines if a DAE is QL in its leading derivatives. Our method is suitable for an implementation through operator overloading or source code translation.

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References

  1. Nedialkov, N.S., Pryce, J.D.: Solving differential-algebraic equations by Taylor series (II): computing the system Jacobian. BIT. 47(1), 121–135 (2007)

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  2. Nedialkov, N.S., Pryce, J.D.: Solving differential-algebraic equations by Taylor series (III): the DAETS code. JNAIAM 3(1–2), 61–80 (2008)

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  3. Nedialkov, N.S., Pryce, J.D., Tan, G.: DAESA—a MATLAB tool for structural analysis of DAEs: software. ACM Trans. Math. Softw. (2013). Accepted for publication

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  4. Pryce, J.D.: A simple structural analysis method for DAEs. BIT 41(2), 364–394 (2001)

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  5. Pryce, J.D., Nedialkov, N.S., Tan, G.: DAESA—a MATLAB tool for structural analysis of DAEs: Theory. To appear in ACM Transactions on Mathematical Software (2014)

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Author information

Authors and Affiliations

  1. Department of Computing and Software, McMaster University, Hamilton, ON, Canada

    Guangning Tan & Nedialko S. Nedialkov

  2. Cardiff School of Mathematics, Cardiff University, Cardiff, UK

    John D. Pryce

Authors
  1. Guangning Tan
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  2. Nedialko S. Nedialkov
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  3. John D. Pryce
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Corresponding author

Correspondence to Guangning Tan .

Editor information

Editors and Affiliations

  1. Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, Canada

    Monica G. Cojocaru

  2. Dept of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Department of Mathematics and MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roman N. Makarov

  4. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roderick V. N. Melnik

  5. MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Hasan Shodiev

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© 2015 Springer International Publishing Switzerland

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Tan, G., Nedialkov, N., Pryce, J. (2015). A Simple Method for Quasilinearity Analysis of DAEs. In: Cojocaru, M., Kotsireas, I., Makarov, R., Melnik, R., Shodiev, H. (eds) Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science. Springer Proceedings in Mathematics & Statistics, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-12307-3_64

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