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ODE treatment of PDE
Posted:
Feb 12, 2012 4:28 PM


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.
Is there a significant difficulty with this approach?



