Solving differential-algebraic equations by Taylor series (I): Computing Taylor coefficients

Nedialkov, N. S. and Pryce, John D. ORCID: https://orcid.org/0000-0003-1702-7624 2005. Solving differential-algebraic equations by Taylor series (I): Computing Taylor coefficients. BIT Numerical Mathematics 45 (3) , pp. 561-591. 10.1007/s10543-005-0019-y

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	differential-algebraic equations (DAEs); structural analysis; Taylor series; automatic differentiation
Publisher:	Springer Verlag
ISSN:	0006-3835
Last Modified:	21 Oct 2022 10:17
URI:	https://orca.cardiff.ac.uk/id/eprint/39682

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