Imposing boundary conditions to a shooting method

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pxg882 2013-1-15

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https://ww2.mathworks.cn/matlabcentral/answers/58827-imposing-boundary-conditions-to-a-shooting-method

I am shooting a 5th order system for {F,F',G,G',H}(all of which are functions of the similarity variable eta) specifying the conditions F(0)=0, G(0)=1, H(0)=0. I need to impose the following two boundary conditions at some suitably large eta_infty.

F'-nF/eta(n-1)=0 and G'-nG/eta(n-1)=0 at eta=eta_infty (where n is a constant)

Is there a way of doing this using the ode45 solver? I have a shooting script using the ode45 solver that works but I cannot figure out a way to incorporate these two conditions into my script. I've tried solving this using the boundary value problem solver but the system of equations is quite complex and the required integration range is large meaning that the boundary value solver fails in this case.

Any help and insight anybody could give me would be greatly appreciated.

Paul