Re: NDSolve and Piecewise

• To: mathgroup at smc.vnet.net
• Subject: [mg92113] Re: NDSolve and Piecewise
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 20 Sep 2008 05:00:07 -0400 (EDT)
• References: <gavt1g\$g61\$1@smc.vnet.net>

```Hi,

foo[t_?NumericQ] :=
Piecewise[{{t/10, 0 <= t < 5}, {(10 - t)/10, 5 <= t < 10}}]

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

??

Regards
Jens

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?
>
> Thanks,
>
> Marshall
>

```

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