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