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shooting method, boundary value problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113764] shooting method, boundary value problem
  • From: Regina <regina.lagrasta at googlemail.com>
  • Date: Thu, 11 Nov 2010 06:09:51 -0500 (EST)

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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