document: Differential algebraic systems anew It is proposed to figure out the leading term in differential algebraic systems more precisely . Low index linear systems with those properly stated leading terms are considered in detail . In particular , it is asked whether a numerical integration method applied to the original system reaches the inherent regular ODE without conservation , i.e. , whether the discretization and the decoupling commute in some sense . In general one can not expect this commutativity so that additional difficulties like strong stepsize restrictions may arise . Moreover , abstract differential algebraic equations in infinite-dimensional Hilbert spaces are introduced , and the index notion is generalized to those equations . In particular , partial differential algebraic equations are considered in this abstract formulation
doc_bio_tags: B I I O O O O O O O O O O O B I I O O O B I I I O O O O O O O O O O O O O O O O O O O B I I O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B I O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: differential algebraic systems low index linear systems numerical integration method inherent regular ode commutativity stepsize restrictions abstract differential algebraic equations