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Re: shooting method, boundary value problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg113798] Re: shooting method, boundary value problem
*From*: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
*Date*: Sat, 13 Nov 2010 00:59:38 -0500 (EST)
*References*: <ibgitq$e87$1@smc.vnet.net>
This looks like normal modes for sound propagation in a waveguide. At
any rate, you have a 2nd order differential equation with two
conditions. This leads to a unique solution. If you are looking for
normal modes, you probably need to think about solving the more general case
y''[x]+alpha*y[x]==0
For different values of alpha. Here is my attempt.
Manipulate[
Y = y /. NDSolve[{y''[x] + \[Alpha] y[x] == 0, y[1] == 0,
y'[1] == a}, y, {x, 0, 1}][[1]];
Plot[Y[x], {x, 0, 1}, PlotRange -> {-10, 10}]
,
{a, -20, 20}, {\[Alpha], 0, 500, .1}
]
used initial conditions at the far end and then manipulate a and alpha.
You could do this automatically with a zero finder approach.
Kevin
On 11/11/2010 6:09 AM, Regina wrote:
> hi there,
> im trying to solve a more involved differential equation that has a
> whole family of solutions. so i started with a similar and more simple
> example:
>
> Manipulate[
> Plot[Evaluate[{y[x]} /.
> NDSolve[{y''[x] + y[x] == 0, y'[0] == 0, y[1] == 0}, y, x,
> Method -> {"Shooting",
> "StartingInitialConditions" -> {y[0] == b, y'[0] == a}}]], {x,
> 0, 1}, PlotRange -> All], {a, 0, 3}, {b, 0, 3}]
>
> what i basically want is to get all the sinusoidal modes by varying
> 'some' parameter. i want to be able to tune one parameter so that i
> get the mode with zero nods, one nod, two nods etc. how do i do that?
>
> (i know that mathematica can solve this equation analytically, but as
> mentioned above, this is just an example for a more involved
> calculation.)
>
> thanks for your help.
> r.
>
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