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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 UTC5, 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(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 > > 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.



