Solving differential-algebraic equations by Taylor series (II): Computing the System Jacobian

Nedialkov, N. S. and Pryce, John D. ORCID: https://orcid.org/0000-0003-1702-7624 2007. Solving differential-algebraic equations by Taylor series (II): Computing the System Jacobian. BIT Numerical Mathematics 47 (1) , pp. 121-135. 10.1007/s10543-006-0106-8

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Abstract

The authors have developed a Taylor series method for solving numerically an initial-value problem differential-algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit, BIT, 45 (2005), pp. 561–592. Numerical results have shown that this method is efficient and very accurate. Moreover, it is particularly suitable for problems that are of too high an index for present DAE solvers. This paper develops an effective method for computing a DAE’s System Jacobian, which is needed in the structural analysis of the DAE and computation of Taylor coefficients. Our method involves preprocessing of the DAE and code generation employing automatic differentiation. Theory and algorithms for preprocessing and code generation are presented. An operator-overloading approach to computing the System Jacobian is also discussed.

Item Type:	Article
Date Type:	Publication
Status:	Published
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/39681

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