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


$y(a)=y_0$ 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.

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


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This comes up in the citations and looks like it might be worth a peek: – Steve Huntsman Jan 29 '11 at 21:18
In theoretical chemistry, there is a trick known as the 'initial value representation' from W. H. Miller that is used in semiclassical quantum dynamics to solve the time-dependent Schrodinger equation (approximately). Perhaps some of the ideas in there might be of interest to a general analysis audience. – Jiahao Chen Jan 31 '11 at 1:28

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