[Axiom-math] Numeric ODE and DAE solvers

[Daniel Herring]

Hi all,

I am interested in using Axiom for my work.  This involves (symbolically) 
deriving the dynamic equations for robotic models, using these to design 
control strategies, and then using simulations to evaluate control 
performance.  These models are highly nonlinear with no closed-form 
solutions.  A simple example might be a double-pendulum, only activated at 
the center joint, balancing and impacting against rigid surfaces.

In general, the models come from Euler-Lagrange equations, resulting in 
differential algebraic equations of the form 
A(x,x',t)*x''+B(x,t)*x'+C(x,t)==0, where x is a vector.  A is usually 
invertible, and so these can be converted to ordinary differential 
equation form.

Currently, I use Mathematica to do everything, but I would like to move 
away from it for several reasons -- cost and certain "won't fix" bugs 
being two of them.  To handle impacts, I have been simulating until after 
the impact occurs, interpolating the solution to find the exact impact 
time, and then proceeding accordingly.

Matlab, Scilab, and Octave are undesirable for this work, mainly because 
of their reduced support for symbolic expressions.  However, the symbolic 
packages such as Axiom don't seem to have numeric differential equation 
solvers built in...  I'm hoping this is something I have just missed, but 
the story seems to be ... NAG libraries ... $$.

If this is something missing from Axiom, then how hard would it be to 
remedy?  At first, I thought of interfacing directly to Scilab or Octave, 
but a little investigation shows that these simply use the ODEPACK, LSODE, 
and DASPK libraries.  All three libraries are written in Fortran.

So here are my questions:
- Is the best solution to interface Axiom directly with these Fortran 
libraries?
- If so, are there any comments as to which library is "the best" as far 
as functionality, efficiency, and accuracy?
- Would modifying the NAG library link be a good way to proceed?

Thanks for your help,
Daniel