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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.