numerical methods – Finite Difference Scheme for non-linear PDE

I’ve been trying to find a finite difference scheme for the 1D partial differential equation as follows:

$$frac{partial F}{partial t}=frac{partial}{partial x} (( frac{partial F}{partial x})^k)$$

However I have not found any material on how to construct one for a non-linear function such as this one. I have tried a few methods however without knowledge of how the steps in space occur in a function such as this I am unsure of their accuracy. Any comment on the stability of such a scheme would also be very useful.

Thanks!