The additional Dynamics of Least Squares Completions for Linear Differential Algebraic Equations
by
Irfan Okay
PhD Student, North Carolina State Univeristy, Department of Mathematics
Coauthors: Stephen Campbell, Peter Kunkel

Many physical problems are most easily initially modelled as a nonlinear implicit system of differential algebraic equations (DAE). However, DAE's contain difficulties that are not present when working with ODE's.

There are several approaches proposed for solving higher index DAE's numerically for which the more classical methods may fail. One of these approaches is called explicit integration (EI). The method is based on forming a derivative array by differentiating the DAE a number of times and solving the system using least squares methods. The result is a computed ODE whose solutions contain the solutions of the DAE. This ODE is then integrated using a classical numerical method to get to the soltuions of the DAE. However, the additional dynamics of the least squares completion can affect the numerical soltuions.

In this work, we first determine the additional dynamics of least squares completions of linear DAE's and then introduce different modifications of the derivative array for which the additional dynamics do not affect the numerical integration.

Date received: September 24, 2007