A New Look at Dummy Derivatives for Differential-Algebraic Equations

Abstract

We show the dummy derivatives index reduction method for DAEs, introduced in 1993 by Mattsson & Söderlind, is a particular case of the Pryce $\varSigma$-method solution scheme. We give a pictorial display of the underlying block triangular form.

This approach gives a simple general method to cast the reduced system in semi-explicit index 1 form, combining order reduction and index reduction in one process.

It also shows each DD scheme for a given DAE is uniquely described by an integer “DDspec” vector $\boldsymbol{\delta }$.

The method is illustrated by an example.

We give various reasons why, contrary to common belief, converting further from semi-explicit index 1 form to an explicit ODE, can be a good idea for numerical solution.