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

  • Guangning Tan
  • Nedialko S. Nedialkov
  • John D. Pryce
Conference paper


Systems of differential-algebraic equations (DAEs) 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.



The authors acknowledge with thanks the financial support for this research: GT is supported in part by the Ontario Research Fund, Canada, NSN is supported in part by the Natural Sciences and Engineering Research Council of Canada, and JDP is supported in part by the Leverhulme Trust, the UK.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Guangning Tan
    • 1
  • Nedialko S. Nedialkov
    • 2
  • John D. Pryce
    • 3
  1. 1.School of Computational Science and EngineeringMcMaster UniversityHamiltonCanada
  2. 2.Department of Computing and SoftwareMcMaster UniversityHamiltonCanada
  3. 3.School of MathematicsCardiff UniversityCardiffUK

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