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

Guangning Tan (), Nedialko S. Nedialkov () and John D. Pryce ()
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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

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 763-773 from Springer

Abstract: 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.

Keywords: Differential Algebraic Equation System; Solvable DAEs; MapleSim; Pantelides; Modelica Language (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-30379-6_68

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