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## [Axiom-math] Numeric ODE and DAE solvers

**From**: |
Daniel Herring |

**Subject**: |
[Axiom-math] Numeric ODE and DAE solvers |

**Date**: |
Tue, 13 Dec 2005 00:45:44 -0600 (CST) |

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

**[Axiom-math] Numeric ODE and DAE solvers**,
*Daniel Herring* **<=**