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Update applicable equation

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Max Luebke 2022-04-20 10:06:38 +02:00
parent 777d75baa5
commit f42af515fb
1 changed files with 8 additions and 2 deletions
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@ -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) & = 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} \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 #+NAME: eqn:5
\begin{equation}\displaystyle \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} \end{equation}
In case of constant right boundary, the finite difference of point In case of constant right boundary, the finite difference of point