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I'm looking to solve the following system of equations with boundary conditions using the shooting method in MATLAB:

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 want to also be able to find the solution using the shooting method as well.

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!