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Topic: ODE treatment of PDE
Replies: 6   Last Post: Mar 7, 2012 8:52 PM

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 Pierre Asselin Posts: 82 Registered: 12/8/04
Re: ODE treatment of PDE
Posted: Feb 12, 2012 7:22 PM

Gib Bogle <g.bogle@auckland.ac.nz> 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