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:
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If we consider FEM we get,
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Thus, we can rewrite Equation 140 as
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here
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