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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(i1) 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 CrankNicolson.
> 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



