On 16/02/2012 3:03 a.m., firstname.lastname@example.org 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.