# [Maxima] numerical sol'n of vector ODE

sen1 at math.msu.edu sen1 at math.msu.edu
Mon Jan 8 23:42:34 CST 2007

```You just want to plot parametrized curves in 3-space.

plot3d lets you plot expressions of the form

t -> [x(u,v), y(u,v), z(u,v)]

If the functions x(u,v), y(u,v), z(u,v) do not depend on v, then you
have a curve parametrized by u.

so, e.g.

plot3d([t, t^2, t^3], [t,0,1], [s,0,1]);

gives a plot of the curve over the square [0,1] x [0,1] in 3-space.

If you put the mouse in the window and move it, you can rotate the
curve in 3-space.

To solve your DE numerically, you would use a solver (e.g. like
runge-kutte).

There is a rk routine in the contrib packages written by Jaime
Villate (I only have used it for 2-d vector fields).

Try

? rk;

HTH,
-sen

> I have a modestly complicated ODE in 3-space, complicated enough that
> there is no closed form solution.  I would like to see a numerical
> solution through a given initial point.  That is given dx/dt = A . x
> (where x is a 3 vector) and an initial point x0, I'd like to get
> maxima to compute the trajectory through x0 and show me a 3d plot.
> Does maxima know how to do this?
>
> thanks!
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>

--
---------------------------------------------------------------------------
| Sheldon E. Newhouse            |    e-mail: sen1 at math.msu.edu           |
| Mathematics Department         |       				   |
| Michigan State University      | telephone: 517-355-9684                |
| E. Lansing, MI 48824-1027 USA  |       FAX: 517-432-1562                |
---------------------------------------------------------------------------
```