Consistent Initial Condition Calculation for Differential-Algebraic Systems

In this paper we describe a new algorithm for the calculation of consistent initial conditions for a class of systems of differential-algebraic equations which includes semi-explicit index-one systems. We consider initial condition problems of two types---one where the differential variables are specified, and one where the derivative vector is specified. The algorithm requires a minimum of additional information from the user. We outline the implementation in a general-purpose solver DASPK for differential-algebraic equations, and present some numerical experiments which illustrate its effectiveness.