Re: [Phys-l] accurate numerical solution of equations of motion

[John Denker <jsd@av8n.com>]

On 11/04/2009 07:52 AM, Vern Lindberg wrote:

> I see two approaches. Both have their merits.
>
> 1. Learn how to do your own coding to solve the DE in a language of  
> your choice, Excel, C, Basic, Fortran, ...
>
> 2. Use a package that does the grunt work for the numerical solutions  
> and provides nice outputs including graphs and visualizations.

Yes!  Both have their merits.  That's an important point, 
and well said.

Some thought like that was part of the motivation for
starting this thread.  It's been gnawing at me.  I knew 
there was something else that needed to be said, but I 
couldn't put my finger on it.  Thanks.

At the next level of detail:

 *) The merits of approach (2) should be obvious.

 *) The merits of approach (1) include:
  -- It's a pedagogical starting point, i.e. a good way 
   for students to get their feet wet.  It's easy enough 
   to be doable, yet hard enough to teach some respect 
   for how much the canned solvers are doing for you.
  -- It has lasting value in that it teaches you how to
   more wisely use the canned solvers, many of which 
   have lots of adjustable parameters.
  -- For some applications, the canned solvers just
   don't work.  Sometimes you need to write your own
   special-purpose integrator (perhaps by modifying 
   pre-existing open-source routines).
  -- Last but not least, somebody has to write the
   canned general-purpose integrators.  Somebody has
   to understand how this is done.


>  For  
> this Maple, Mathematica do th trick, although they are not always  
> cheap. For free you can get either VPython or Easy Java Simulations.  
> For an example of the latter, here is a rigid body rotator done in EJS
> http://faculty.ifmo.ru/butikov/Applets/Precession.html


There are at least four matlab-like programs:
 -- matlab itself ($$$)
 -- scliab (free, open source)
 -- octave (free, open source)
 -- Rlabplus (free, open source)


A quick rundown on the choices can be found at
  http://www.dspguru.com/sw/opendsp/mathclo2.htm