I genuinely do not understand the Newton-Kantorovich method for BVPs :(

114 Views Asked by At

I've been struggling to wrap my head around the concept of the Newton-Kantorovich method and the steps necessary to approximate a solution to a BVP:

y" = f(x,y,y') on the interval a $\leq$ x $\leq$ b, with boundary conditions y(a) = $\alpha$ , y(b) = $\beta$

I've read these different articles on the method:

https://core.ac.uk/download/pdf/82133838.pdf

https://hal.archives-ouvertes.fr/hal-01313209/file/adly2016.pdf

https://en.wikipedia.org/wiki/Kantorovich_theorem

But I still cannot grasp the concept. If any of you can please provide me with a simpler explanation or an example, it would be much much appreciated.