Solving Differential-Algebraic Equations by Taylor Series (I): Computing Taylor Coefficients |
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| Authors: | Email author" target="_blank">Nedialko S?NedialkovEmail author Email author" target="_blank">John D?PryceEmail author |
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| Institution: | (1) Department of Computing and Software, McMaster University, Hamilton, Ontario, L8S 4L7, Canada;(2) Computer Information Systems Engineering Department, Cranfield University, RMCS Shrivenham, Swindon, SN6 8LA, UK |
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| Abstract: | This paper is one of a series underpinning the authors’ DAETS code for solving DAE initial value problems by Taylor series
expansion. First, building on the second author’s structural analysis of DAEs (BIT, 41 (2001), pp. 364–394), it describes
and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may be
fully implicit, nonlinear, and contain derivatives of order higher than one. Algorithmic details are given.
Second, it proves that either the method succeeds in the sense of computing TCs of the local solution, or one of a number
of detectable error conditions occurs.
AMS subject classification (2000) 34A09, 65L80, 65L05, 41A58 |
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| Keywords: | differential-algebraic equations (DAEs) structural analysis Taylor series automatic differentiation |
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