On 04/02/2013 07:57 AM, mystiro at gmail.com wrote:
> Hello,
>
> I'm struggling with a non ordinary differential equation analogous to a
> diffusion equation:
>
> 'diff(f,t) = -K * 'diff(f,x) + r * (1 - f/f0) * f^2 ;
f is I guess a function of t and x, so that this is a partial
differential equation. To get anything useful out of it you will need
initial conditions f(0,x).
I have had some success in maxima using series solutions for this type
of thing. write f(t,x) = sum(A[i]*g[i](x),i,1,16) for example, for some
chosen basis functions g, there are orthogonal polynomials in the
"orthopoly" package for example, and then do explicit or implicit
time-stepping of the A[i] coefficients by hand, either using
collocation, or by approximating the integrals by quadpack functions...
it's not terribly hard, but it isn't something that's automatically
built-in.