Strange solution of NDSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg45134] Strange solution of NDSolve
- From: Yama Masu <yamagomas at yahoo.co.jp>
- Date: Wed, 17 Dec 2003 07:54:47 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hi.
I am now trying to solve string oscillation with impulse using NDSolve.
f[x_, t_] = f[(t > 0 && t < 0.011) && (x > -0.01 && x < 0.01), Sin[100 Pi t], 0]
sol = NDSolve[{D[u[x, t], {t, 2}] == D[u[x, t], {x, 2}] + f[x, t],
u[x, 0] == 0, Derivative[0, 1][u][x, 0] == 0, u[-1, t] == 0,
u[1, t] == 0}, u, {x, -1, 1}, {t, 0, 1}]
{usol} = {u} /. sol[[1]]
Plot[usol[x, 0.2], {x, -1, 1}, PlotRange -> {0, 0.001}]
But NDSolve gives strange solutions in the following two ways.
(1)
If I change the boundary to -2<x<-2 such that
...u[-2, t] == 0, u[2, t] == 0}, u, {x, -2, 2}, {t, 0, 1},
The solution is different from the one shown above and is about the double.
But this is physically strange. Since the speed of propagation of the wave is 1,
there must be no effect of boundary until t=1. There should not be any
difference between the two above.
Why does NDSolve give dependence on boundary at small t?
(2)
If I change the boundary to -3<x<1 such that
...u[-3, t] == 0, u[1, t] == 0}, u, {x, -3, 1}, {t, 0, 1},
The singularity at x=0 is neglected and NDSolve gives u[x,t]=0.
How can I have NDSolve recognize this singularity?
Yama Masu