ray tracing - how to numerically integrate the equation of the ray

In a continuous isotropic medium having refractive index n, (not constant)
the ray path can be described by the following equation

d/ds(n dr/ds)) = grad (n)

with an obvious meaning of the symbols (for they who can help me!).

I wrote a code to calculate the ray path. I found result qualitatively consistent but not quantitatively. I think that the integration procedure I used is wrong (I used a simple one,
that I set up on my own).

Can anybody help me?
Can anybody suggest me a paper or book where to read an algorithm?
Has anybody a source code to integrate it? (I would need just the core instructions).

Thanks Bye