Think of it like a solver for many coupled differential equations.
The coupling happens through "linear" equality constraints.
Such as "the output pressure variable of component A needs to be equal the input pressure variable of component B".
Something that Modelica doesn't do very well is stochastic systems. There you would need to go into SDE and that brings a lot of technicalities.
[1] Petzold, Linda R. Description of DASSL: a differential/algebraic system solver. No. SAND-82-8637; Sandia National Labs, 1982.
[2] Kunkel, Peter. Differential-algebraic equations: analysis and numerical solution. European Mathematical Society, 2006.
Think of it like a solver for many coupled differential equations. The coupling happens through "linear" equality constraints. Such as "the output pressure variable of component A needs to be equal the input pressure variable of component B".
Something that Modelica doesn't do very well is stochastic systems. There you would need to go into SDE and that brings a lot of technicalities.
[1] Petzold, Linda R. Description of DASSL: a differential/algebraic system solver. No. SAND-82-8637; Sandia National Labs, 1982.
[2] Kunkel, Peter. Differential-algebraic equations: analysis and numerical solution. European Mathematical Society, 2006.