Diana Estévez Schwarz, René Lamour
The Computation of Consistent Initial Values for Nonlinear Index-2 Differential-Algebraic Equations
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

65L05 Initial value problems

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Abstract: The computation of consistent initial values for differential-algebraic equations
(DAEs) is essential for staring a numerical integration. Based on the tractability index concept a method is proposed to filter those equations of a system of index-2 DAEs, whose differentiation leads to an index reduction.
The considered equation class covers Hessenberg-systems and the equations arising from the simulation of electrical networks by means of Modified Nodal Analysis (MNA). The index reduction provides a method for the computation of the consistent initial values.
The realized algorithm is described and illustrated by examples.
Keywords: Differential-Algebraic Equation, DAE, Index, Consistent Initial Values, Consistent Initialization, Circuit Simulation, Modified Nodal Analysis, MNA, Algorithm