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. 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.
References
Pantelides algorithm Wikipedia(Text) CC BY-SA