Consistency of general point conditions for DAE systems

This paper addresses the issue of consistency of general point conditions imposed on nonlinear DAE systems. Such conditions represent a generalisation of initial conditions in that they may involve values of the dependent variables at several distinct values of the independent variable. They appear in a variety of practical applications such as those involving periodic conditions or where a degree of “shaping” of the transient behaviour of a particular system is desired. A necessary condition is derived that has to be satisfied for a set of general point conditions to be consistent with each other and with the underlying DAE system. This permits the formulation of a structural algorithm that is applicable to large nonlinear DAE system of index 1.