More Complex Boundary Conditions with ODE-BVPs

4 MORE COMPLEX BOUNDARY CONDITIONS WITH ODE-BVPs 

Consider again the problem of heat transfer in a rod, where the ODE is 

However, now assume that the left boundary is still exposed to boiling water, but that the right side is insulated (no heat flow). From Fourier s law of heat conduction, 

The shooting method can be used to solve this problem with no difficulty by transforming the second-order ODE into two first-order ones with one of the variables being the temperature gradient. That is, define F such that 

In the shooting method, the procedure is to assume a value for F(0) and shoot for 

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