Pantelides algorithm: Difference between revisions

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'''Pantelides algorithm''' givesin [[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>Francois Cellier, ''[http://www.ece.arizona.edu/~cellier/ece449_lecture.html Lecture notes about Pantelides algorithm]''</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.

{{Context|date=August 2010}}

'''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.<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>Francois Cellier, ''[http://www.ece.arizona.edu/~cellier/ece449_lecture.html Lecture notes about Pantelides algorithm]''</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.

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>