From e4ec0a11dad15249909404de38b5de7874fe4254 Mon Sep 17 00:00:00 2001 From: Marco De Lucia Date: Tue, 27 Dec 2022 15:37:41 +0100 Subject: [PATCH] MDL fixing docs --- doc/ADI_scheme.org | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/ADI_scheme.org b/doc/ADI_scheme.org index 5cfa8b0..e0d2abd 100644 --- a/doc/ADI_scheme.org +++ b/doc/ADI_scheme.org @@ -418,8 +418,8 @@ approximation of $\frac{\partial}{\partial x} \left(\alpha(x) \left\{ \begin{aligned} \frac{C^{t+1/2}_{i,j}-C^{t }_{i,j}}{\Delta t/2} = & \frac{1}{\Delta x^2} \left[ \alpha_{i+1/2,j} C^{t+1/2}_{i+1,j} - (\alpha_{i+1/2,j}+\alpha_{i-1/2,j}) C^{t+1/2}_{i,j} + \alpha_{i-1/2,j} C^{t+1/2}_{i-1,j}\right] + \\ - & \frac{1}{\Delta y^2} \left[ \alpha_{i,j+1/2}C^{t}_{i,j+1} - (\alpha_{i,j+1/2}+\alpha_{i,j-1/2}) C^t_{i} + \alpha_{i,j-1/2}C^{t}_{i,j-1}\right]\\ -\frac{C^{t+1 }_{i,j}-C^{t+1/2}_{i,j}}{\Delta t/2} = & \frac{1}{\Delta y^2} \left[ \alpha_{i+1/2,j}C^{t+1/2}_{i+1,j} - (\alpha_{i+1/2,j}+\alpha_{i-1/2,j}) C_{i} + \alpha_{i-1/2,j}C^{t+1/2}_{i-1,j}\right] + \\ + & \frac{1}{\Delta y^2} \left[ \alpha_{i,j+1/2}C^{t}_{i,j+1} - (\alpha_{i,j+1/2}+\alpha_{i,j-1/2}) C^t_{i,j} + \alpha_{i,j-1/2}C^{t}_{i,j-1}\right]\\ +\frac{C^{t+1 }_{i,j}-C^{t+1/2}_{i,j}}{\Delta t/2} = & \frac{1}{\Delta y^2} \left[ \alpha_{i+1/2,j}C^{t+1/2}_{i+1,j} - (\alpha_{i+1/2,j}+\alpha_{i-1/2,j}) C^t_{i,j} + \alpha_{i-1/2,j}C^{t+1/2}_{i-1,j}\right] + \\ & \frac{1}{\Delta x^2} \left[ \alpha_{i,j+1/2}C^{t+1}_{i,j+1} - (\alpha_{i,j+1/2}+\alpha_{i,j-1/2}) C^{t+1}_{i,j} + \alpha_{i,j-1/2}C^{t+1}_{i,j-1}\right] \end{aligned} \right.