Rafael de Pelegrini Soares
Fri, 18 Dec 2009 04:09:50 -0800
Dear Arquimedes and Francesco, In a numerical sense, the solution of a index-reduced problem is not the same of the original high-index problem. This is because the reduced index problem accepts more solutions than the original one (algebraic constraints are replaced by differential equations). This is known as the "drift-off" effect. Please check "Hairer, E. and Wanner, G., Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer-Verlag, 1996." for more details on that effect.
Just my 2 cents. 2009/12/17 Arquimedes Canedo <can...@gmail.com>: > Francesco, > > > Thanks for the insightful answers. > > >> The solution of an initial value problem for a higher index DAE and for the >> same DAE brought to index 1 with Pantelides / Dummy Derivatives is exactly >> the same. > > This is good news. The only place where we could have numerical error > is then the numerical solver itself. > >> If the implicit algebraic equations have a unique solution in closed form, a >> symbolic manipulator could solve them symbolically and replace them with >> their closed-form solution. Otherwise, you typically use numerical, >> Newton-like solvers, which require to know the residuals of the implicit >> equations, and possibly their Jacobian w.r.t. the unknowns. > > This sounds familiar, at least that is what Scicos/Simulink try to > handle the algebraic loops. > I guess this is all explained in detail in the books you have > recommended before. I'll try to get my hands on them soon. > > > Thanks, > > Arquimedes > -- Prof. Rafael de Pelegrini Soares, D.Sc Chemical Engineering Department - UFRGS raf...@enq.ufrgs.br, rafael....@gmail.com office: +55 51 3308 3528