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\begin{multline}tilde{\overline{P}}= \overline{P}_{n}+\bigtriangleup z \left [\left \{ \frac{\overline{a}_{n}\gamma_{n}+j(\Omega _0 - \Omega_{f}\gamma _{n})\overline{P}_{n}}{u_{z,n}} \right \} \right+ jMag_{n}\overline{P}_{n} ]\\\overline{u}_{z,n+1}= \overline{u}_{z,n} + \Delta z \left \{\left( -\frac{|\overline{p}_{n}|^{2}}{\overline{u}_{z,n}} \right).Mag_{n} \overline{p}_{n} \right \}\\\tilde{\gamma}_{n+1} = \frac{1}{\sqrt {1-(v/c)^{2}}} =\sqrt{1+\tilde{u}^{2}_{z,n+1}+|\tilde{\overline{p}}_{n+1}|^{2}}\\\overline{p}_{n+1}=\overline{p}_{n} + \frac{\Delta z}{2}\left [\left ( \frac{\overline{a}_{n+1}\gamma_{n}+j(\Omega _0 - \Omega_{f}\gamma _{n+1})\tilde{\overline{P}}_{n+1}}{u_{z,n+1}} + jMag_{n+1}\tilde{\overline{P}}_{n+1}\right ) + \left(\frac{\overline{a}_{n}\gamma_{n}+j(\Omega _0 - \Omega _{f}\gamma_{n})\overline{P}_{n}}{u_{z,n}} + j Mag_{n}\overline{P}_{n}\right) \right ]\end{multline}