"Computing Taylor series and associated Jacobians for DAEs"

J. Pryce

Abstract:

The speaker's Structural Analysis method for differential-algebraic
equation (DAE) systems provides an algorithm for generating the Taylor
series of the solution, and thus a method of numerical solution. Ned
Nedialkov has implemented this in a C++ code.  Numerical results will be
presented showing the code is both fast and accurate on some standard test
problems.

The method does not work for all DAEs. It succeeds, roughly speaking, if
the sparsity structure of the description of the DAE correctly represents
its mathematical structure. Recognizing success/failure, when the DAE is
described by computer code, is crucial for the practical usefulness of the
method.

Therefore, the talk will describe recent work by Nedialkov and Pryce that
proves the method is more robust than we realized. Namely, it fails if and
only if the "system Jacobian"  of the DAE is structurally singular up to
roundoff - something that is easily recognized in practice.