The additional dynamics of least squares completions for linear differential algebraic equations (Q998187)

The present paper deals with the numerical treatment of linear differential algebraic equations (DAEs) of higher index. The authors suggest to derive the essential underlying ordinary differential equation (ODE) and to construct a completion of it on an open subset. These completions are not unique for higher index DAEs and their extra dynamics depend on the choice of the linear algebra. The completed ODE can then be integrated numerically with a suitable standard ODE integrator. Nevertheless, the additional dynamics of the completion can affect the numerical solution of the DAE. The present paper analyzes this extra dynamics in the case of least squares completions of linear invariant DAEs.