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: <email@example.com>
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 >