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Re: Why does the Shooting Method fail?

• To: mathgroup at smc.vnet.net
• Subject: [mg95701] Re: Why does the Shooting Method fail?
• From: "Frank Kampas" <fkampas at verizon.net>
• Date: Sun, 25 Jan 2009 06:51:49 -0500 (EST)
• References: <gl721c$c95$1@smc.vnet.net>

The shooting method can fail for non-linear differential equations because
the solution becomes singular for some values of the initial conditions.  In 
such cases, quasi-linearization is a better approach.

http://library.wolfram.com/conferences/conference98/abstracts/iterative_solution.html


"SK" <skhushrushahi at gmail.com> wrote in message 
news:gl721c$c95$1 at smc.vnet.net...
> Hi
>
> I have a set of coupled nonlinear differential equations with boundary
> conditions that I am solving using the shooting method. The
> mathematica notebook can be downloaded at
>
> http://web.mit.edu/~shahriar/Public/submission2.nb
>
> In the line where eqn2 is defined I show that if eta' is 0.1 the
> shooting method works and the boundary conditions of vz[xend]==0 and w
> [xend]==0 is satisfied. If I change the eta' to 0.01 (which is a case
> I do want) I dont get it to converge to these boundary conditions.
>
> I have tried numerous things like changing the stepsize, number of
> steps and even reverse shooting and it doesnt work. I have even
> changed the range for the variables A and B that determine the
> starting slope of vz[x] and w[x] but that doesnt do much.
>
> I would greatly appreciate it if someone can help me on this matter.
> Thanks
> Shahriar
>