Solution for Cauchy Problem

[Klaus Duellmann]

I wonder if an implicit scheme solution in the form of an Octave 
program already 
exists for the follwong parabolic pde:

Find f in C^2,1 solving 

        df/dt + a df/dx + 1/2 b^2 d^2f/dx^2 + c f = 0

where   - f, a, b and c are functions of x and t
        - x real, t in [0, T[
with a boundary condition f(x,T) = g(x).

A solution for an extended problem where x is no longer a scalar 
but a two-dimensional vector would 
be even more helpful.
If somebody has a code (e.g. a Crank-Nicholson scheme) I would be 
really grateful because this would save me some time at a crucial 
moment. Thanks a lot in advance!

Klaus

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