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NDSolve solution does not fulfill boundary condition ??

• To: mathgroup at smc.vnet.net
• Subject: [mg121115] NDSolve solution does not fulfill boundary condition ??
• From: Alex <axel.kowald at gmail.com>
• Date: Mon, 29 Aug 2011 03:47:29 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello everybody,

I use Mathematica 7 and try to solve and plot a 2nd order ODE like this:

sol = NDSolve[{0 == 4800*O2''[x] + 1500*Exp[-(100*x)^2] - 2000*O2[x],
O2'[-0.5] == 0, O2'[0.5] == 0}, O2, {x, -1, 1}]
Plot[O2[x] /. sol, {x, -1, 1}, PlotRange -> All]

The solution looks ok, i.e. the slope of the solution is 0 at 0.5 and
-0.5, as required by the boundary conditions. But if I slightly change
the parameter values from 1500 to 1000 like this:

sol = NDSolve[{0 == 4800*O2''[x] + 1000*Exp[-(100*x)^2] - 2000*O2[x],
O2'[-0.5] == 0, O2'[0.5] == 0}, O2, {x, -1, 1}]

I get a solution with slope=0 at -0.5, but with a positive slope at
0.5 !!??

How can this be ?  What am I doing wrong ?

Many thanks,

axel

• Follow-Ups:
  • Re: NDSolve solution does not fulfill boundary condition
    • From: Oliver Ruebenkoenig <ruebenko@wolfram.com>