Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Gib Bogle Posts: 42 Registered: 3/28/11
Re: ODE treatment of PDE
Posted: Feb 16, 2012 3:27 AM

On 16/02/2012 3:03 a.m., mirko.vukovic@gmail.com 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.