Simulation of system models containing zeroorder causal paths  I. Classification of zeroorder causal paths
Dijk, J. van and Breedveld, P.C. (1991) Simulation of system models containing zeroorder causal paths  I. Classification of zeroorder causal paths. Journal of the Franklin Institute, 328 (56). pp. 959979. ISSN 00160032

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Abstract:  The existence of zeroorder causal paths in bond graphs of physical systems implies the set of state equations to be an implicit mixed set of Differential and Algebraic Equations (DAEs). In the block diagram expansion of such a bond graph, this type of causal path corresponds with a zeroorder loop. In this paper the numerical solution of the DAEs by methods commonly used for solving stiff systems of Ordinary Differential Equations (ODEs) is discussed. Apart from a description of the numerical implications of zeroorder causal paths, a classification of zeroorder causal paths is given with respect to the behavior of the numerical solution method. This behavior is characterized by “the index of nilpotency” (Gear and Petzold, Siam J. Numerical Anal., Vol. 21, No. 4, 1984). Propositions concerning the index of nilpotency and the class of zeroorder causal path are formulated. These propositions are illustrated by examples. The concept “essential causal cycle” is introduced as a special, closed, causal path which cannot be eliminated. 
Item Type:  Article 
Copyright:  © 1991 Elsevier 
Faculty:  Engineering Technology (CTW) Electrical Engineering, Mathematics and Computer Science (EEMCS) 
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Link to this item:  http://purl.utwente.nl/publications/72924 
Official URL:  http://dx.doi.org/10.1016/00160032(91)90064A 
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