diff --git a/doc/ADI_scheme.org b/doc/ADI_scheme.org index 8a3fd92..557fe34 100644 --- a/doc/ADI_scheme.org +++ b/doc/ADI_scheme.org @@ -163,11 +163,17 @@ C_0^{j+1} & = C_0^{j} + \frac{\alpha \cdot \Delta t}{\Delta x^2} \cdot \left( C & = C_0^{j} + \frac{\alpha \cdot \Delta t}{\Delta x^2} \cdot \left( C^{j+1}_{1}- 3 C^{j+1}_{0} +2l \right) \end{align} -Which leads to the following term applicable to our approach: +Now we define variable $s_x$ as following: + +\begin{equation} + s_x = \frac{\alpha \cdot \Delta t}{\Delta x^2} +\end{equation} + +Substituting with the new variable $s_x$ and reordering of terms leads to the equation applicable to our model: #+NAME: eqn:5 \begin{equation}\displaystyle - -C^j_0} = \left[\frac{\alpha \cdot \Delta t}{\Delta x^2}\right] \cdot \left(C^{j+1}_1 + 2l \right) + \left[ -1 - 3 \cdot \frac{\alpha \cdot \Delta t}{\Delta x^2} \right] \cdot C^{j+1}_0 + -C^j_0} = s_x \cdot C^{j+1}_1 + (2s_x) \cdot l + (-1 - 3s_x) \cdot C^{j+1}_0 \end{equation} In case of constant right boundary, the finite difference of point