Recent Advances in Algorithmic Differentiation by Shaun Forth Paul Hovland Eric Phipps Jean Utke & Andrea Walther

Author:Shaun Forth, Paul Hovland, Eric Phipps, Jean Utke & Andrea Walther
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

2 Applying PSM

We believe that many problems can be converted into IVODEs of polynomial form, as demonstrated in the following examples.

2.1 Example 1: PSM and AD Applied to an IVODE

Consider the IVODE

(1)

for some complex valued α. This problem highlights the properties of PSM and AD because it has the closed form solution

(2)

and because it can be posed in several equivalent polynomial forms. This is not a problem that most would consider immediately amenable to standard power series methods. A simple recursive relationship generates the Taylor coefficients for yα given by

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