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Re: ODE treatment of PDE
Posted:
Feb 15, 2012 9:03 AM
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On Sunday, February 12, 2012 7:22:41 PM UTC-5, Pierre Asselin wrote:
> Gib Bogle <email address deleted> wrote:
> > I'm showing my ignorance by asking this question, but here goes...
>
> > It's possible to represent a discretised PDE by a system of ODEs. For
> > example, the simple 1D diffusion equation
>
> > dC/dt = k.d2C/dx2 (where derivatives are partial)
>
> > can be represented on a grid of points with spacing h by
>
> > dC(i)/dt = K.(C(i-1) -2.C(i) + C(i+1))/h^2
>
> > With suitable treatment of initial and boundary conditions, this ODE
> > system could be solved with one of several methods.
>
> Such as Crank-Nicolson.
>
> > Is there a significant difficulty with this approach?
>
> Stability of the chosen ODE scheme. But otherwise no, it's often
> done that way.
>
> --
> pa at panix dot com
I have heard of the "method of lines". But I don't know much about it.
Mirko
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