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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,

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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.
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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.
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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.
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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 ... \$\$.
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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.
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So here are my questions:
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- 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

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