Between Quasilinear and LTI DAE - Details
2007 (English)Report (Other academic)
Methods for index reduction of general nonlinear differential-algebraic equations are generally difficult to implement due to the recurring use of functions defined only via the implicit function theorem. By adding structure to the equations, these implicit funcitons may become possible to implement. In particular, this is so for the quasilinear and linear time-invariant (LTI) structures, and it turns out that there exists an algorithm for the quasilinear form that is a generalization of the shuffle algorithm for the LTI form in the sense that, when applied to the LTI form, it reduces to the shuffle algorithm. For this reason, the more general algorithm is referred to as a quasilinear shuffle algorithm. One can then say that the LTI form is invariant under the quasilinear shuffle algorithm, and it is expected that the algorithm can be fruitfully tailored to take care of the structural information in any such invariant form. In this paper a class of forms ranging from quasilinear to LTI DAE is searched for forms that are invariant under the quasilinear shuffle algorithm, and it is suggested that this kind of survey be extended to a more complete mapping between index reduction algorithms and their invariant forms.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2007. , 18 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2764
Differential-algebraic, Quasilinear, Shuffle algorithm, Invariant
IdentifiersURN: urn:nbn:se:liu:diva-56128ISRN: LiTH-ISY-R-2764OAI: oai:DiVA.org:liu-56128DiVA: diva2:316973