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Re: Shooting Problem

• To: mathgroup@smc.vnet.net
• Subject: [mg10490] Re: Shooting Problem
• From: Wojciech Budzianowski <wbudzian@iic.pwr.wroc.pl>
• Date: Tue, 20 Jan 1998 02:22:41 -0500
• Organization: I-13 PWr
• References: <69nbig$89l@smc.vnet.net>

Alex Tabarrok wrote:
> 
> Hello,
>        I have a system of two differential equations, k'[t] and c'[t].
> In the problem I am working with I know the initial condition for k,
> k[0]=a and I know a steady state or boundary condition k[sometime]=b.
> The problem is to choose c[0] so that k[t] arrives (sometime) at point
> b (which is a steady state).  In puttering around with this problem
> I've been use NDSolve to generate paths beginning at k[0]=a and c[0]=x.
> Then  by trial and error I vary x until I have a path such that
> k[sometime] reaches b or very near b.  Obviously, I would like an
> interative procedure to do this automatically.  Has anyone written such
> a procedure already?  I beleive this method of solving this type of
> problem is called the shooting method.
> 
> Thanks
> --
> Alex Tabarrok
> Department of Economics
> Ball State University
> Muncie, IN, 47306
> EMail: 00ATTabarrok@BSUVC.BSU.Edu
> Web Page: http://www.bsu.edu/econ then hit Faculty and then Tabarrok

Hi Alex,
It is possible to solve ODE with boundary conditions. The succes depends
much on the type of the system of ODE. If this is linear You may use
any iterative procedure(bisection,linear aproximation, Marquardt
optimisation method etc.) to find a new values of intial conditions.
But if the system is highly nonlinear You will probably fail as I did
with mine(instead I used own-written procedures and some sophisticated
software).
Good luck.
-- 
---------------------------------------------------- Wojciech
Budzianowski
wbudzian@iic.pwr.wroc.pl
http://www.iic.pwr.wroc.pl/~wbudzian Phone Work +48 +71 3203625
Institute of Chemical Engineering and Heat Equipment Wroclaw University
of Technology
Wroclaw, Poland
Norwida 4/6    50-373 Wroclaw
----------------------------------------------------