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.