Simplification of Differential Algebraic Equations by the Projection Method

Reduction of a differential algebraic equation (DAE) system to an ordinary differential equation system (ODE) is an important step in solving the DAE numerically. When the ODE is obtained, an ODE solution technique can be used to obtain the final solution. In this paper we consider combining index reduction with projection onto the constraint manifold. We show that the reduction benefits from the projection for DAEs of certain form. We demonstrate that one of the applications where DAEs of this form appear is optimization under constraints. We emphasize the importance of optimization problems in physical systems and provide an example application of the projection method to an electric circuit formulated as an optimization problem where Kirchhoff’s laws are acting as constraints.