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# Pantelides algorithm

Pantelides algorithm gives a systematic method for reducing high-index systems of differential-algebraic equations to lower index, by selectively adding differentiated forms of the equations already present in the system.[1][2][3] 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.[4][5][6]]

References

C Pantelides, 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)

Francois Cellier, Lecture notes about Pantelides algorithm

John Pye, Pantelides Algorithm in PHP (source code in PHP language)

Peter A. Fritzson, Principles of Object-Oriented Modeling and Simulation with Modelica 2.1, Wiley, ISBN 0-471-47163-1

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.

EMSO a free-to-use closed-source simulator/equation solver that includes implementation for the Pantelides algorithm.

1 Examples of spectral methods

1.1 A concrete, linear example

1.1.1 Algorithm

1.2 A concrete, nonlinear example

2 A relationship with the spectral element method

3 See also

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