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Symbolic-Numeric Methods for Improving Structural Analysis of Differential-Algebraic Equation Systems

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

Listed:
  • Guangning Tan

    (McMaster University, School of Computational Science and Engineering)

  • Nedialko S. Nedialkov

    (McMaster University, Department of Computing and Software)

  • John D. Pryce

    (Cardiff University, School of Mathematics)

Abstract

Systems of differential-algebraic equations (DAEs) Structural analysis of differential-algebraic equations are generated routinely by simulation and modeling environments, such as MapleSim and those based on the Modelica language. Before a simulation starts and a numerical method is applied, some kind of structural analysis is performed to determine which equations to be differentiated, and how many times. Both Pantelides’s algorithm and Pryce’s Σ-method are equivalent in the sense that, if one method succeeds in finding the correct index and producing a nonsingular Jacobian for a numerical solution procedure, then the other does also. Such a success occurs on many problems of interest, but these structural analysis methods can fail on simple, solvable DAEs and give incorrect structural information including the index. This article investigates Σ-method’s failures and presents two symbolic-numeric conversion methods for fixing them. Both methods convert a DAE on which the Σ-method fails to a DAE on which this SA may succeed.

Suggested Citation

  • Guangning Tan & Nedialko S. Nedialkov & John D. Pryce, 2016. "Symbolic-Numeric Methods for Improving Structural Analysis of Differential-Algebraic Equation Systems," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 763-773, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_68
    DOI: 10.1007/978-3-319-30379-6_68
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