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

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Gib Bogle

Posts: 42
Registered: 3/28/11
ODE treatment of PDE
Posted: Feb 12, 2012 4:28 PM
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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.

Is there a significant difficulty with this approach?

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