winstead@faraday.ECE.CMU.EDU (Charles Holden Winstead) (02/19/91)
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