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arXiv · 1608.06691

Conversion Methods for Improving Structural Analysis of Differential-Algebraic Equation Systems

Guangning Tan·Nedialko S. Nedialkov·John D. Pryce
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Abstract

Differential-algebraic equation systems (DAEs) are generated routinely by simulation and modeling environments. Before a simulation starts and a numerical method is applied, some kind of structural analysis (SA) is used to determine which equations to be differentiated, and how many times. Both Pantelides's algorithm and Pryce's $\Sigma$-method are equivalent: if one of them finds correct structural information, the other does also. Nonsingularity of the Jacobian produced by SA indicates a success, which occurs on many problems of interest. However, these methods can fail on simple, solvable DAEs and give incorrect structural information including the index. This article investigates $\Sigma$-method's failures and presents two conversion methods for fixing them. Both methods convert a DAE on which the $\Sigma$-method fails to an equivalent problem on which this SA is more likely to succeed.

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BibTeXRIS

Guangning Tan, Nedialko S. Nedialkov, John D. Pryce. 2016-08-24. Conversion Methods for Improving Structural Analysis of Differential-Algebraic Equation Systems. https://arxiv.org/abs/1608.06691

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