Zwarty koniec linii
i₁(k) = G_fu₁(k) - G_fu₂(k-m) - i₂(k-m)
u₂(k) = u₂(k-m) = 0
i₁(k) = G_fu₁(k) - i₂(k-m)
i₂(k) = - G_fu₁(k) - i₁(k-m)
i₂(k-m) = - G_fu₁(k-2m) - i₁(k-2m)
i₁(k) = G_fu₁(k) + G_fu₁(k-2m) + i₁(k-2m)
Otwarty koniec linii
i₁(k) = G_fu₁(k) - G_fu₂(k-m) - i₂(k-m)
i₂(k) = i₂(k-m) = 0
i₁(k) = G_fu₁(k) - G_fu₂(k-m)
i₂(k) = G_fu₂(k) - G_fu₁(k-m) - i₁(k-m) = 0
G_fu₂(k) = G_fu₁(k-m) + i₁(k-m)
G_fu₂(k-m) = G_fu₁(k-2m) + i₁(k-2m)
i₁(k) = G_fu₁(k) - G_fu₁(k-2m) - i₁(k-2m)


RL niejawna metoda Eulera
u(k) = u_R(k) + u_L(k)
u_R(k) = $\frac{1}{G_{R}}i\left( k \right)$
u_L(k) = $\frac{1}{G_{L}}\left( i\left( k \right) - j_{L}\left( k - 1 \right) \right)$
u(k) = $\frac{1}{G_{R}}i\left( k \right)$ + $\frac{1}{G_{L}}\left( i\left( k \right) - j_{L}\left( k - 1 \right) \right)$
u(k) = $\frac{1}{G_{R}}i\left( k \right)$ + $\frac{1}{G_{L}}i\left( k \right)$ – $\frac{1}{G_{L}}j_{L}\left( k - 1 \right)$
u(k) = $\frac{1}{G_{R}G_{L}}i\left( k \right)$ – $\frac{1}{G_{L}}j_{L}\left( k - 1 \right)$
i(k) = G_RG_Lu(k) + G_Rj_L(k−1)
G = $\frac{G_{R}R_{L}}{G_{R} + G_{L}}\ $= $\frac{T}{L + LT}$
j(k-1) = $\frac{G_{R}j_{L}\left( k - 1 \right)}{G_{R} + G_{L}}$ = $\frac{j_{L}\left( k - 1 \right)}{R\left( \frac{1}{R} + \frac{T}{L} \right)}$ = .. = $\frac{\text{Li}\left( k - 1 \right)}{L + RT}$

RC niejawna metoda Eulera
u(k) = u_R(k) + u_C(k)
u_R(k) = $\frac{1}{G_{R}}i\left( k \right)$
u_C(k) = $\frac{1}{G_{C}}\left( i\left( k \right) - j_{C}\left( k - 1 \right) \right)$
u(k) = $\frac{1}{G_{R}}i\left( k \right)$ + $\frac{1}{G_{C}}\left( i\left( k \right) - j_{C}\left( k - 1 \right) \right)$
u(k) = $\frac{1}{G_{R}}i\left( k \right)$ + $\frac{1}{G_{C}}i\left( k \right)$ – $\frac{1}{G_{C}}j_{C}\left( k - 1 \right)$
u(k) = $\frac{1}{G_{R}G_{C}}i\left( k \right) - \ \frac{1}{G_{C}}j_{C}\left( k - 1 \right)$
G =$\ \frac{G_{R}R_{C}}{G_{R} + G_{C}}\ $= $\frac{C}{T + RC}$
j(k-1) = $\frac{G_{R}j_{C}\left( k - 1 \right)}{G_{R} + G_{C}}$ = $\frac{j_{C}\left( k - 1 \right)}{R\left( \frac{1}{R} + \frac{C}{T} \right)}$ = $\frac{\text{Tj}\left( k - 1 \right)}{T + RC} = \ \ $
$= \frac{T}{T + RC} - Gu(k - 1)$


RL jawna metoda Eulera
i(k) = i(k-1) + $\frac{T}{L}u_{L}(k)$
u_L(k) = u(k) - u_R(k)
u_R(k) = Ri(k)
i(k) = i(k-1) + $\frac{T}{L}$(u(k) - Ri(k))
i(k) = i(k-1) + $\frac{T}{L}$u(k) - $\frac{\text{RT}}{L}$i(k)
(1-$\frac{\text{RT}}{L})i\left( k \right) = i\left( k - 1 \right) + \ \frac{T}{L}u(k)$
i(k) = $\frac{T}{L + RT}u(k)$ + $\frac{L}{L + RT}\ $i(k-1)
i(k) = Gu(k) + j(k-1)
j(k-1) = $\frac{L}{L + RT}\ $i(k-1) G=$\frac{T}{L + RT}$

RC jawna metoda Eulera
u_C(k) = u_C(k-1) + $\frac{T}{C}\ $i(k)
u_C(k) = u(k) – u_R(k) = u(k) – Ri(k)
u(k) – Ri(k) = u(k) + u(k-1) – Ri(k-1)
Ri(k) + $\frac{T}{C}i(k)$ = u(k) – u(k-1) + Ri(k-1)
i(k)(R +$\ \frac{T}{C}$) = u(k) – u(k-1) + Ri(k-1)
i(k) = $\frac{C}{T + RC}u(k)$ - $\frac{C}{T + RC}u(k - 1)$ + $\frac{\text{CR}}{T + RC}i(k - 1)$
i(k) = Gu(k) + j(k-1)
G = $\frac{C}{T + RC}$ j(k-1) = $- \frac{C}{T + RC}u(k - 1)$ + $\frac{\text{CR}}{T + RC}i(k - 1)$

RL metoda trapezów
i(k) = i(k-1) + $\frac{T}{2L}$u_L(k)
u_L(k) = u(k) – u_R(k)
u_R(k) = Ri(k)
i(k) = i(k-1) + $\frac{T}{2L}$(u_L(k) + u_L(k-1))
i(k) = i(k-1) + $\frac{T}{2L}$(u(k) – Ri(k) + u(k-1) – Ri(k-1))
i(k) = i(k-1) + $\frac{T}{2L}$u(k) - $\frac{\text{TR}}{2L}$i(k) + $\frac{T}{2L}$u(k-1) - $\frac{\text{TR}}{2L}$i(k-1)
i(k)(1+$\frac{\text{TR}}{2L})\ $= i(k-1) + $\frac{T}{2L}$u(k) + $\frac{T}{2L}$u(k-1) - $\frac{\text{TR}}{2L}$i(k-1)
i(k) = i(k-1)($\frac{2L - RT}{2L + RT}$) + $\frac{T}{2L + RT}$u(k) + $\frac{T}{2L + RT}$u(k-1)
i(k) = Gu(k) + j(k-1)
G = $\frac{T}{2L + RT}$ j(k-1) = Gu(k-1) + ($\frac{2L - RT}{2L + RT}$)i(k-1)



RC metoda trapezów
u_C(k) = u_C(k-1) + $\frac{T}{2C}$(i_C(k) + i_C(k-1))
u_C(k) = u(k) – u_R(k) = u(k) – Ri(k)
u(k) – Ri(k) = u(k-1) – Ri(k-1) + $\frac{T}{2C}$(i_C(k)+ i_C(k-1))
Ri(k) + $\frac{T}{2C}i\left( k \right)$= u(k) - u(k-1) + Ri(k-1) - $\frac{T}{2C}\ $i(k-1)
i(k)(R +$\ \frac{T}{2C}$) = u(k) – u(k-1) + Ri(k-1) - $\frac{T}{2C}$ i(k-1)
i(k) = $\frac{2C}{2RC + T}$u(k) - $\frac{2C}{2RC + T}$u(k-1) + $\left( \frac{2RC - T}{2RC + T} \right)i(k - 1)$
i(k) = Gu(k) + j(k-1)
G = $\frac{2C}{2RC + T}$ j(k-1) = - $\frac{2C}{2RC + T}$u(k-1) + $\left( \frac{2RC - T}{2RC + T} \right)i(k - 1)$