Using the Shooting Method

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pxg882
pxg882 2012-10-30
Hi all,
I'm looking to solve the following system of equations with boundary conditions using the shooting method:
F''=F^2-G^2+F'H
G''=2FG+G'H
H'=-2F
along with the conditions F(0)=0, G(0)=1, H(0)=0, F(infinity)=0, G(infinity)=0.
I've found the solution using the BVP4C solver but need to also be able to find the solution using the shooting method.
I'm really quite new to MATLAB and don't really know where to start!
Any help anyone can give me would be greatly appreciated. Thanks!

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回答（1 个）

Titus Edelhofer
Titus Edelhofer 2012-10-30
The first thing to do is independent of the programming: reformulate your second order system by a (larger) first order system. Once you have that, use e.g. ode45 to solve it.
Titus
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Titus Edelhofer
Titus Edelhofer 2012-11-2
If you have two unknowns I would use e.g. fminsearch where your objective function is the error (quadratic difference) between the target (coming from the "other" boundary condition) and the values you get at the end of the shoot (via ode45).
pxg882
pxg882 2012-11-8
Thanks for your input,
I think I'm just about there with this now.
I feel it was my limited MATLAB knowledge that was letting me down. Still things should get better with time and practice!

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