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Solving (nonlinear) equations in modeling tools

I am interested in how a modeling tool (in my case OpenModelica and Dymola - the Modelica modeling language) solves systems of equations (linear and / or non-linear). These tools are designed to solve differential algebraic equations. I know a little about the theory of transformation of a system of differential algebraic equation into ODE (keyword "index-reduction"). My questions:

  • How do these tools solve a system of equations without differential equations? Is the system still converted (index reduction) in ODE?
  • What if I have a model with multiple algebraic equations and multiple ODEs - but they are not related?

Many thanks.

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OpenModelica will use an equidistant time grid based on the number of output time points (or the number of intervals) and solve the algebraic system for each of these time points.



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The basics of converting equations to assignments are very well covered in slide decks 1-6 from Professor Selye's lecture in Zurich ETH: https://www.inf.ethz.ch/personal/fcellier/Lect/MMPS/Refs/mmps_refs.html

You will find additional links at the end of each lecture.



The only difference for systems without differential equations is that you have no state variables, the rest works the same.

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