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Numerical Methods pp 120–127Cite as

Singular implicit ordinary differential equations and constraints

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1005))

Abstract

Implicit ordinary differential equations, also known as differential/algebraic equations, arise naturally in a number of formulations. These are frequently singular and can cause considerable numerical difficulty. We do not know how to handle the general problem, but a common formulation leads to equations that can be integrated in some cases.

Supported by the U.S. Department of Energy, Grant DOEAC0276ER02383 and by the U.S. DOE Office of Basic Energy Sciences.

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References

  1. Gear, C. W., The simultaneous numerical solution of differential-algebraic equations, IEEE Trans. Circuit Theory TC-18, (1), 1971, 89–95.

    Article  Google Scholar 

  2. Gear, C. W. and L. R. Petzold, Differential/algebraic systems and matrix pencils, Proc. Conference on Matrix Pencils, Pitea, Sweden, March 1982. also, Dept. Rpt. UIUCDCS-82-1086, Dept. Computer Sci., Univ. Illinois, Urbana, 1982.

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  3. Gear, C. W. and L. R. Petzold, ODE methods for the solution of differential/algebraic systems, Dept. Rpt. UIUCDCS-82-1103, Dept. Computer Sci., Univ. Illinois, Urbana, 1982.

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  4. Lötstedt, Per, A numerical method for the solution of mechanical systems with unilateral constraints, Report TRITA-NA-7920, Royal Inst. Technology, Stockholm, 1979.

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  5. Sincovec, R. F., Dembart, B., Epton, M. A., Erisman, A. M., Manke, J. W. and E. L. Yip, Solvability of large-scale descriptor systems, Final Report DOE Contract ET-78-C-01-2876, Boeing Computer Services Co., Seattle, WA.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, 61801-2987, Urbana, IL

    C. W. Gear

  2. Applied Mathematics Division, Sandia National Laboratories, 94550, Livermore, CA

    L. R. Petzold

Authors
  1. C. W. Gear
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  2. L. R. Petzold
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© 1983 Springer-Verlag

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Gear, C.W., Petzold, L.R. (1983). Singular implicit ordinary differential equations and constraints. In: Numerical Methods. Lecture Notes in Mathematics, vol 1005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0112529

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  • DOI: https://doi.org/10.1007/BFb0112529

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12334-7

  • Online ISBN: 978-3-540-40967-0

  • eBook Packages: Springer Book Archive

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