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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
Re: ODE treatment of PDE
Posted: Feb 16, 2012 3:27 AM
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On 16/02/2012 3:03 a.m., wrote:
> 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

I've since learned that the 1D PDE solver in Matlab, pdepe, does exactly
what I described. It uses the solver ode15s.

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