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From Luc Maisonobe <Luc.Maison...@free.fr>
Subject [math] improvement of the ODE package
Date Tue, 08 Jul 2008 20:35:32 GMT
In order to solve issue MATH-172 and for other related needs, I have
started work on the ordinary differential equations package as some of
you may have noticed.

The first phase was simple cleaning: reorganizing the package that was
becoming quite huge. There are now several subpackages:
 - nonstiff which provides integrators (and continuous output
   interpolators) for non-stiff problems
 - sampling which deals with step handlers (fixed and variable steps)
 - events which deals with discrete events (what used to be called
   switching functions in the previous version)

The second phase is under development: introducing new simple multistep
integrators: fixed step explicit Adams-Bashforth, fixed step implicit
Adams-Moulton and BDF, still for non-stiff problems. This is a little
harder than I thought at first, because I really want this integrators
to provide the same rich features as the existing ones: multiple
discrete events handling, continuous output, events handlers. I also
wanted a user customizable autostart feature (multistep methods need
some help to get started). I did not find any reference to continuous
output models for these simple integrators, so I had to develop the
underlying equations myself. I hope to check a few new classes soon.
Meanwhile, I also have to change a little the shared API with the
existing integrators, in order to get a consistent package.

The third phase will consist in implementing integrators able to handle
stiff problems. I will probably start with a port of LSODE (from netlib,
available under a BSD type license) which is based on GEAR method.

Luc


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