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MathGroup Archive 1992

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Differential Equations and Mathematica

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Differential Equations and Mathematica
  • From: pmcguire at coral.bucknell.edu
  • Date: Wed, 11 Nov 1992 14:20:53 -0500

I need to decide whether or not to use Mathematica (or some other software
package) in a differential equations class next semester.  When Mathematica
first appeared it was lacking in a lot of areas with regard to differential
equations.  I would like to know if the situation has improved and if
anyone has used Mathematica successfully for such a task.  Additionally, if
anyone has developed useful packages appropriate for an undergraduate ODE
class I would appreciate some help.  Some specific uses I had in mind are
as follows:

1.  Plot two dimensional vector fields with overlaid solution curves.
2.  Solve second order linear equations with constant coefficients where
the forcing function varies.
3.   Consider numerical and graphical solutions to nonlinear problems and
compare the results to the solutions obtained using a linear approximation
method.

The PlotField.m package that comes with Mathematica suffers from two
difficulties with regard to (1).  First it is slow and cumbersome to use
and second I don't know (probably my fault) a way of easily having
Mathematica fit some solution curves to the vector field.  With regard to
(2) I have (in the past) had considerable difficulty getting Mathematica to
solve nonhomogeneous equations of type (2) with very simple forcing
functions.
If Mathematica is not appropriate for this kind of use does anyone wish to
go out on a limb and suggest something else?  (I would prefer a Macintosh
application but am not close minded.)

Thanks in advance,
Paul
 






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