A New Look at Dummy Derivatives for Differential-Algebraic Equations

John D. Pryce () and Ross McKenzie ()
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John D. Pryce: Cardiff University, School of Mathematics
Ross McKenzie: Cardiff University, School of Mathematics

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 713-723 from Springer

Abstract: Abstract We show the dummy derivatives index reduction method for DAEs, introduced in 1993 by Mattsson & Söderlind, is a particular case of the Pryce Σ $$\varSigma$$ -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 δ $$\boldsymbol{\delta }$$ . 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.

Keywords: Ordinary Differential Equation; Implicit Function Theorem; State Item; Index Reduction; Ordinary Differential Equation System (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_64

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DOI: 10.1007/978-3-319-30379-6_64

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