I am new to the topic of differential-algebraic-equations:
$ \dot x = f(x,u,c) $
where $u$ are control variables and $c$ algebraic variables.In my first literature study i found two approaches:
- given $x$ and $u$, solve (if non-linear with Newton) $0=g(x,u,c)$ for $c$. Make a step (Euler for instance)
- Index reduction: derive algebraic equations with respect to time - so that in the end you get a normal ODE wich can be solved with ordinary ODE solver.
Why lead differntial algebraic equations to stiff ODE's?: "From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations"
Most of literature that i found talk about method 2; is it method 1 not simpler? Or do I misunderstood something :)? Could you recommend basic literature (simple introduction) to this topic?
Thank you very much!