Thank you for any pointers,
Helmut Jarausch
See the work of Ned Nedialkov on Hermite-Obreshkov methods
Ned finished at Toronto last summer, and is now at McMaster. His Toronto e-mail address is ned@cs.toronto.edu. I do not seem to have his new address.
You can find several of his reports at www.cs.toronto.edu/NA/reports.html
Once page I found is a paper abstract: www.maths.uq.edu.au/~kb/scicade99/abstract/NedNedialkov8.html
Perhaps Ned will pick up on this response and contribute current pointers.
You should also contact Markus Neher at the University of Karlsruhe. He has done recent work on alternatives to the explicit Euler stepsize control.
Note also that if you overcome the explicit Euler step used for initial enclosure, the standard methods of Lohner, Staunung, and Nedialkov perform better for stiff problems than you might expect because in Algorithm II for tightening the enclosure, they use similar Jacobian information to the point methods for stiff problems.
George F. Corliss
If you have a question related to validated computing, interval analysis, or related matters, I recommend