Pantelides algorithm: Difference between revisions

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'''Pantelides algorithm''' in [[mathematics]] is a systematic method for reducing high-index systems of [[Differential algebraic equation|differential-algebraic equations]] to lower index. This is accomplished by selectively adding differentiated forms of the equations already present in the system.<ref>C Pantelides, [https://dx.doi.org/10.1137/0909014 The Consistent Initialization of Differential-Algebraic Systems], SIAM J. Sci. and Stat. Comput. Volume 9, Issue 2, pp.&nbsp;213–231 (March 1988) (the original paper where the algorithm is described)</ref><ref>{{cite web|first=Francois|last=Cellier|archive-url=https://web.archive.org/web/20060909005029/http://www.ece.arizona.edu/~cellier/ece449_ppt6.pdf|archive-date=2006-09-09|url=http://www.ece.arizona.edu/~cellier/ece449_ppt6.pdf|url-status=dead|title=The Structural Singularity Removal Algorithm by Pantelides|work=ECE 449/549: Lecture Notes|date=Fall 2003}}</ref><ref>John Pye, ''[http://jpye.dyndns.org/pantelides/ Pantelides Algorithm in PHP] {{webarchive|url=https://web.archive.org/web/20110413074018/http://jpye.dyndns.org/pantelides/ |date=2011-04-13 }}'' (source code in [[PHP]] language)</ref> It is possible for the [[algorithm]] to fail in some instances.

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'''Pantelides algorithm''' gives a systematic method for reducing high-index systems of [[Differential algebraic equation|differential-algebraic equations]] to lower index, by selectively adding differentiated forms of the equations already present in the system. It is possible for the algorithm to fail in some instances.

Pantelides algorithm is implemented in several significant equation-based simulation programs such as gPROMS, [[Modelica]] and [[EMSO simulator|EMSO]].<ref>Peter A. Fritzson, ''Principles of Object-Oriented Modeling and Simulation with Modelica 2.1'', Wiley, {{ISBN|0-471-47163-1}}</ref><ref>R de P. Soares and A R. Secchi, 2005, ''Direct initialisation and solution of high-index DAE systems'', Computer Aided Chemical Engineering '''20''', {{doi|10.1016/S1570-7946(05)80148-8}}.</ref><ref>[http://www.enq.ufrgs.br/trac/alsoc/wiki/EMSO EMSO] a free-to-use closed-source simulator/equation solver that includes implementation for the Pantelides algorithm.</ref>

== Further reading ==

==References==

* C Pantelides, [http://dx.doi.org/10.1137/0909014 The Consistent Initialization of Differential-Algebraic Systems], SIAM J. Sci. and Stat. Comput. Volume 9, Issue 2, pp. 213-231 (March 1988) (the original paper where the algorithm is described)

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* [http://www.ece.arizona.edu/~cellier/ece449_lecture.html Lecture notes by Francois Cellier]

* An [http://pye.dyndns.org/pantelides/ open-source implementation of Pantelides algorithm] in the [[PHP]] language

* [http://www.enq.ufrgs.br/trac/alsoc/wiki/EMSO EMSO] a free-to-use closed-source simulator/equation solver that includes implementation for the Pantelides algorithm.

[[Category:Numerical differential equations]]

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