PDECOL Example:

Supposed one wanted to solve the following system of partial differential equations on the interval [0,1].

with boundary conditions of

and

With initial conditions given by

This corresponds to the first example in the original reference to PDECOL (given above). This is quite simple to solve with the pdecol gateway in octave. The user must specify a F.m function expressing the PDE in the following form

And our boundary conditions in the form

Once in this form the octave code requires derivative of each side with respect to its arguments. For this problem these are coded in the octave functions DBDU_BNDRY.m, DBDUX_BNDRY.m, and DZDT_BNDRY.m. The function names give indications to as to what derivative is being taken. Finally the user must specify the initial conditions in a function UINIT.m.

Once this is done a call to the core routine looks like pdecol_Script.m. Finally we can reap the benefits by viewing the solution to our problem

Note that all code for this example (duplicating what is found in the links above) can be found in the directory EG1 included with the pdecol source.

John Weatherwax

Last modified: Mon Sep 25 09:02:03 EDT 2006