Hello

Is there any methods available for transforming a 2nd order Boundary value problem such as

$F\left(x,y,\frac{\text{dy}}{\text{dx}},\frac{d^2y}{\text{dx}^2}\right)=0$

$y(a)=y_0$ and $y(b)=y_1$

into an initial value problem? I know this is possible for linear ODEs.

I also know of the shooting method (a numerical technique).

But I've often seen people make transformations or change of variables, which manage to convert the BVP into an IVP. I was wondering does anyone know or have any references to how one would go about finding such a transformation?

This author seems to have made some progress on the matter. http://www.jstor.org/stable/2027813

Is there any others people know of? Or transformations for that work for particular nonlinear problems people are aware of.

Regards