Pantelides algorithm in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

is a systematic method for reducing high-index systems of differential-algebraic equations to lower index. This is accomplished by selectively adding differentiated forms of the equations already present in the system. It is possible for the

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

to fail in some instances. Pantelides algorithm is implemented in several significant equation-based simulation programs such as gPROMS,

Modelica Modelica is an object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems, e.g., systems containing mechanical, electrical, electronic, hydraulic, thermal, control, electric power or process ...

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

References

Numerical differential equations {{algorithm-stub