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NDSolve and Piecewise

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92085] NDSolve and Piecewise
  • From: "M.G. Bartlett" <marshall.bartlett at gmail.com>
  • Date: Fri, 19 Sep 2008 05:56:59 -0400 (EDT)

Folks,

I am having some trouble with getting Piecewise and NDSolve to play
nicely together.  My problem is to find a solution to the heat flow
equation with an arbitrary time-varying upper boundary condition and a
Neumann-type lower boundary (steady head flow condition).  My code
looks like this:

NDSolve[{D[u[t, x], t] == D[u[t, x], x, x],
  u[t, 0] == Piecewise[{{t/10, 0 <= t < 5}, {(10 - t)/10, 5 <= t <
10}}],
  u[0, x] == x/5, (D[u[t, x], x] /. x -> 5) == 1/5}, u, {t, 0, 10},
{x, 0, 5}]

This returns and NDSolve::ndum error on my system, which past
experience tells me is usually me leaving some symbolic value hanging
around somewhere it ought not to be.  I can't see any such problem
this time.  I'm pretty sure that I have written similar code in the
past (using Piecewise and NDSolve, though it was some time ago and I
can't locate the file now) and had it work, and it works if you
replace Piecewise with another functional form (like Sin[t]).  Am I
missing something?

Thanks,

Marshall


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