Re: NDSolve and Piecewise
- To: mathgroup at smc.vnet.net
- Subject: [mg92126] Re: NDSolve and Piecewise
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Sat, 20 Sep 2008 05:02:34 -0400 (EDT)
- Organization: University of Bergen
- References: <gavt1g$g61$1@smc.vnet.net>
M.G. Bartlett wrote: > 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? > I think that NDSolve attempts to take the derivative of that Piecewise expression symbolically, which results in a function whose value is indeterminate at some points (notably 0 and 5): In[3]:= D[ Piecewise[{{t/10, 0 <= t < 5}, {(10 - t)/10, 5 <= t < 10}}], t] Out[3]= Piecewise[{{0, t < 0}, {1/10, 0 < t < 5}, {-(1/10), 5 < t < 10}, {0, t > 10}}, Indeterminate] The error will go away if you wrap the expression into a function that only evaluates for numerical arguments: bval[t_?NumericQ] := D[Piecewise[{{t/10, 0 <= t < 5}, {(10 - t)/10, 5 <= t < 10}}], t] (Use bval[t] as the boundary condition.)