Parabolic PDE's

[Heber Farnsworth]

Hey out there.  I'm currently working on a project in which I need to solve a 
simple parabolic PDE with an initial condition and some side conditions.  It's 
only in 1 space dimension so it shouldn't be too bad.  The boundary conditions 
are the hard part.

I think that the way to do it would be as an infinite sum of some special 
functions.  As you may know the approach here is to find the special function 
that applies to your PDE and then use the boundary conditions to determine the 
coefficients.  Hopefully the series converges quickly so including the first n 
terms should do.

Octave includes bessel functions which can be used this way but I need some 
others, namely Airy functions and parabolic cylinder functions.  Has anyone 
written any code that does this?  If not I will try it and submit it to octave 
souces (BTW, not enough of us have been doing that!) but I don't want to 
reinvent the wheel if someone has already done it.

Heber Farnworth
Assistant Professor of Finance
the Ohio State University

P.S. I found Airy functions on Netlib so an .oct file could be written to do 
that or it could be compiled in with the source I suppose.