Using the recurrence formula Equation 118, we get:
Here a = 2k0nref .
Using Equation 119 into Equation 131, we get:
Thus,
and,
where
Thus, we can get the unknown field φ l + 1 at z + Δz from the known field φ l solving the triagonal linear system:
If we consider FEM we get,
Thus, we can rewrite Equation 140 as
here
