Hello David,
Thanks for your reply. I have read some papers by Cheb-Terrab and I am familiar with the
routines that he wrote for Maple. I also perused the routines written by Hereman, but decided
to write my own stuff 'from scratch' because of possible copyright issues. It never hurts to look
though.
I noticed that all of Kamke's ode's are available. This is great! I have Kamke's books in my
collection, but having all the ode's available for testing immediately is extremely comfortable.
My first concern right now is to get the Lie point symmetries in an efficient and reliable way.
I focus now on second order ode's and will then extend it to nth order ode's.
However, getting the Lie point symmetries means solving an overdetermined system of partial
differential equations (the linearized symmetry condition). I am now able to solve some simple
pde's and am now working on solving a system of mixed ode's and algebraic relations.
This is where I am stuck right now. I think that in order to efficiently solve a system of ode's
of arbitrary order, mixed with algebraic equations, you need to use differential grobner bases.
I don't know anything about that, so I first have to read a bit about it first (Mansfields thesis is on her website).
I hope it will be trivial to get this working with the grobner package that is implemented.
I'll keep you informed on my progress. If I have working code in need of some criticism, I'll post it here.
Regards,
Nijso
-----Original Message-----
From: RTATECH [mailto:David.Billinghurst at riotinto.com]
Sent: Tue 11/18/2008 12:45 PM
To: Beishuizen, N.A. (CTW); maxima at math.utexas.edu
Subject: RE: [Maxima] contrib_ode
> From: N.A.Beishuizen at ctw.utwente.nl
>
> Is somebody still working on the contrib_ode code?
When I get some time ;-(
All I have done in the last year or so is integrate
Barton Willis's odelin routine and keep the testsuite
up to date. I don't have any code under development.
Contributions gratefully accepted.
> My programming goal is to have a small program that solves
> nonlinear ode's of nth order and systems of nonlinear ode's
> based on point symmetry methods.
> I noticed that contrib_ode already has a Lie symmetry method
> implemented for first order ode's, so maybe somebody else is
> also working on this?
Partially implemented is closer to the truth. The Lie symmetry
method is powerful,but my maxima implementation has weaknesses.
There are plenty of tests commented out in the contrib_ode testsuite.
If you read the references by Cheb Terrab you will see that the
same algorithm gives better results in Maple.
David