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

Several approaches have been proposed for numerically solving lower dimensional, nonlinear, higher index differential algebraic equations (DAEs) for which more classical numerical methods such as backward differentiation or implicit Runge–Kutta may not be appropriate. One of these approaches is called explicit integration (EI). This approach is based on solving nonlinear DAE derivative arrays using nonlinear singular least squares methods. This results in a computed ODE, called the least squares completion, whose solutions contain those of the original DAE. This ODE is then integrated by a classical numerical method. The additional dynamics of the least squares completion can affect the numerical solution of the DAE. This paper begins the study of determining these extra dynamics.