Re: Modified shooting method
- To: mathgroup at smc.vnet.net
- Subject: [mg30511] Re: Modified shooting method
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 24 Aug 2001 20:58:07 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <email@example.com>
- Sender: owner-wri-mathgroup at wolfram.com
eigenvalue problems work not very well with simple shooting
The problem ist, that for a fixed value w[i] you have
- no solution if w[i] is not a eigenvalue
- an infinite number of solutions if w[i] *is* an eigenvalue
The bes solution is to use a double or multiple
shooting method. You should have a look at
file mus.doc mus.doc plus dependencies
by Mattheij and Staarink
for ordinary differential equation boundary-value problem solver
alg multiple shooting
, whence you may also fine DEQNS
gams I1b1 I1b2
An better way may be to use a matrix approach and solve
the matrix eigenvalue problem. The simplest idea is to
us finite differences
y''[x] -> (y[i-1]-2 y[i]+y[i+1])/h^2
for the inner points, and solve
Or to expand the solution in a orthogonal basis you like,
and solve the eigenvalueproblem
Hope that helps
Christophe Le Poncin-Lafitte wrote:
> Sorry for my english, which is poor.
> I'm working about a modelization of cyclonic and anticyclonic structures in
> geophysic ; so this is a study of the nonlinear adjustment of a density
> During our experiment, we observe the adjustment of a cylindrical structure,
> which becomes a little stable lens (during 40s), before the development of
> instabilities. But during the adjustment, we observe the development of
> inertial-gravity waves.
> Now we search to modelize our system.
> Our goal is to quantify the energy of this waves, to evaluate the importance
> of these for the comprehension of the adjustment first, then to understand
> the relative stability of the system, and finally to find why we observe
> instabilities, which destroy the system.
> I have a little problem to solve : a boundary value problem.
> My ODE is quite difficult :
> rap is a parameter, which is a constant. w is the eigenmodes of
> inertial-gravity waves.
> My boundary conditions are : y=0 and y[rap]=0
> I take for initial condition on y' : y'=1.
> In fact, I have to done my shooting on w, to isolate the different
> eigenmodes of inertial-gravity waves. So, this is a modified shooting
> I want to know if anybody has already treat this type of problem ?
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