A new technique for solving high-index differential-algebraic equations using dummy derivatives

A technique for solving high-index problems by combining symbolic and numerical methods is presented. The technique is a variant of index reduction. In the usual manner, parts of the differential-algebraic equation (DAE) are differentiated analytically and appended to the original system. For each additional equation, a derivative is selected to be replaced by a new algebraic variable called a dummy derivative. The resulting augmented system is at most index 1. The dummy derivatives are not subject to discretization; their purpose is to annihilate part of the dynamics in the DAE, leaving only what corresponds to the dynamics of a state-space form. No constraint stabilization is necessary in the subsequent numerical treatment. Numerical tests indicate that the method yields results with an accuracy comparable to that obtained for corresponding state-space ordinary differential equation