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) 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.
Technical report CAS 03-11-NN, Dept. of Computing and Software, McMaster University, Hamilton, ON,
L8S 4L7, Canada, October 2003; also
Technical report DoIS/TR03/03, Computer Information Systems Engineering Dept.,
Cranfield University, RMCS Shrivenham, Swindon SN6 8LA, UK, October 2003.
Download pdf