2016/08/24 by Tan, Guangning, Nedialkov, Nedialko S., Pryce, John D.
#34A09 #41A58 #65L80 #68W30 #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Symbolic Computation (cs.SC)
paper · doi:10.48550/arxiv.1608.06691
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 Σ-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 Σ-method's failures and presents two conversion methods for fixing them. Both methods convert a DAE on which the Σ-method fails to an equivalent problem on which this SA is more likely to succeed.