Second Order Numerical Integration w/ Neumann Boundary Conditions

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a2009
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I hope this is the right place to post this question.

I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C.

I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative I'm stuck.

If anyone could point me in the right direction, or refer me to a text that discusses this problem I'd really appreciate it.
 
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I can add more to this later. But for now check the Numerical Recipe website. www.nr.com Check in the section that has the older versions of the book in pdf format.