On 04/02/2013 03:57 PM, mystiro at gmail.com wrote:
> 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 ;
>
> where K, r and f0 are constants.
>
> I'm not hopping to find an explicit solution but I'd like to be able
> to plot
> it numerically. Is there any method similar to Runge-Kutta for
> non-ordinary
> differential equations ?
Hi,
that equation can be solved by the method of characteristics
(http://en.wikipedia.org/wiki/Method_of_characteristics). Basically, you
will have to solve the following two ordinary differential equations:
dx/dt = K
df/dt = r(1 - f/f0) f
both of which can be solved analytically. The first one gives you the
equation for the characteristics (straight lines in this case) and the
second one tells you how f changes along each of those characteristics.
It could be easy to "build" the solution f(t,x) or not feasible by this
method, depending on the kind of boundary conditions that you have.
That's a feature of partial differential equations: the solution is
highly dependent on the kind of boundary conditions for the problem.
Regards,
Jaime