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From: winstead@faraday.ECE.CMU.EDU (Charles Holden Winstead)
Newsgroups: comp.lang.fortran
Subject: P.D.E.  solver wanted
Message-ID: <1991Feb19.043806.6537@fs7.ece.cmu.edu>
Date: 19 Feb 91 04:38:06 GMT
Sender: news@fs7.ece.cmu.edu (USENET News System)
Organization: Electrical and Computer Engineering, Carnegie Mellon
Lines: 33

I am looking for packages on the network which can solve the following 
partial differential equation.
                     
       d            d  d
       -  (T) - k*  -  - (T) = f(x)u(t)
       dt           dx dx

where u(t) is the unit step function and f(x) is a known forcing function.
Alternatively, an analytical solution would be ideal (:-)), but I can't seem
to get one.  I can solve the homogeneous solution, which is a couple of
erf functions, and I can solve 
                     
                    d  d
              - k*  -  - (T) = f(x)
                    dx dx

say the solution to this is g(x). I can do this. But once I add the u(t),
I can't get a paticular solution.

Any pointer to a solution or a package would be helpful, FORTRAN preferred.
IMSL does this, but the machine I am working on doesn't have and can't 
afford IMSL. :-( .  

In case you're wondering, I get this equation by heating liquid metal with
magnetic fields.  This is the Temperature distribution, with f(x) coming 
from ohmic dissipation of the induced currents.

Thanks

-Charles Winstead
 Carnegie Mellon

 winstead@faraday.ece.cmu.edu