Variable grid mesh in Numerov's method (Fortran)

[Telemachus]

I was trying to implement a variable grid mesh in Numerov's method, while playing with fortran. Numerov method was working well with a standard discretization, but when I tried to implement this variable grid, things came to look as if the 'metric' of the function were depending on the functionality I was using in the grid mesh. I thought that as Numerov's uses two points in the algorithm, that this variable mesh was introducing new things that the standard Numerov algorithm doesn't have in account.

So, basically, I want to know how should I develop an iterative algorithm to work on a variable grid mesh (specifically to solve differential equations), how to tell the algorithm that the previous or forward steps are not at the same distance. Perhaps someone here can help me, or give me some reference. Any textbook that covers this kind of topics?

Thanks in advance.

 

[Telemachus]

After thinking of this, I've realized that I should modify the algorithm I'm using. I think that I should use the chain rule in the derivatives, so in that way I would have the information of how the points in the domain are varying. So, I should take a deeper look at Numerov's method and modify it to adapt to the gridmesh I'm using. Is that correct?

BTW, would this subforum be more appropriate for this topic: https://www.physicsforums.com/forums/programming-and-computer-science.165/ ?