Modified shooting method

• To: mathgroup at smc.vnet.net
• Subject: [mg30489] Modified shooting method
• From: Christophe Le Poncin-Lafitte <christophe.leponcin-lafitte at obspm.fr>
• Date: Fri, 24 Aug 2001 04:05:50 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

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
front.
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 :

y"[x]+q[w,x]*y[x]==0

where
q[w,x]=w^2/(1-BesselI[0,x]/BesselI[0,rap])-1-3/4/r^2-BesselI[1,r]/Bessel[0,r
ap]/r

rap is a parameter, which is a constant. w is the eigenmodes of
inertial-gravity waves.

My boundary conditions are  : y[0]=0 and y[rap]=0
I take for initial condition on y' : y'[0]=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
method.
I want to know if anybody has already treat this type of problem ?

Regards,
Christophe

-----------------------------
Christophe Le Poncin-Lafitte

Observatory of Paris-Meudon
Dpt Atomes et Molécules en Astrophysique

Ecole Normale Supérieure, ENS Ulm
Laboratory of Dynamical Meteorology

```

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