From 5c23b80a84b86893d71ed3fc7dde5afed13b32d2 Mon Sep 17 00:00:00 2001 From: Ubuntu Date: Wed, 24 May 2023 23:11:15 +0000 Subject: [PATCH] Trying to fix another typo, seeing disparities between visual studio markdown and github markdown --- Swift-Hohenberg-Solver/README.md | 23 ++++++++++++++++------- 1 file changed, 16 insertions(+), 7 deletions(-) diff --git a/Swift-Hohenberg-Solver/README.md b/Swift-Hohenberg-Solver/README.md index 3c3be0c..eba572e 100755 --- a/Swift-Hohenberg-Solver/README.md +++ b/Swift-Hohenberg-Solver/README.md @@ -53,7 +53,8 @@ $$\begin{aligned} 1 + \Delta & -1 \end{pmatrix} \begin{pmatrix} - U_n\\ V_n + U_n\\ + V_n \end{pmatrix} &= \begin{pmatrix} U_{n-1} + kg_1U_{n-1}^2 - kU_{n-1}^3\\ 0 @@ -61,13 +62,18 @@ $$\begin{aligned} \end{aligned}$$ As usual, we multiply each side of the equation by a -test function $\overrightarrow\varphi_i = \begin{pmatrix} +test function + +$$\overrightarrow\varphi_i = \begin{pmatrix} \phi_i\\ \psi_i -\end{pmatrix}$ +\end{pmatrix}$$ + +to get the equation $$\begin{aligned} \begin{pmatrix} - \phi_i\\ \psi_i + \phi_i\\ + \psi_i \end{pmatrix}\cdot\begin{pmatrix} 1 - kr & k(1 + \Delta)\\ 1 + \Delta & -1 @@ -75,7 +81,8 @@ $$\begin{aligned} \begin{pmatrix} U_n\\ V_n \end{pmatrix} &= \begin{pmatrix} - \phi_i\\\psi_i + \phi_i\\ + \psi_i \end{pmatrix}\cdot\begin{pmatrix} U_{n-1} + kg_1U_{n-1}^2 - kU_{n-1}^3\\ 0 @@ -86,7 +93,8 @@ and then expand our solution vector in this basis $$\begin{aligned} \sum_j u_j\begin{pmatrix} - \phi_i\\\psi_i + \phi_i\\ + \psi_i \end{pmatrix}\cdot\begin{pmatrix} 1 - kr & k(1 + \Delta)\\ 1 + \Delta & -1 @@ -94,7 +102,8 @@ $$\begin{aligned} \begin{pmatrix} \phi_j\\\psi_j \end{pmatrix} &= \begin{pmatrix} - \phi_i\\\psi_i + \phi_i\\ + \psi_i \end{pmatrix}\cdot\begin{pmatrix} U_{n-1} + kg_1U_{n-1}^2 - kU_{n-1}^3\\ 0 -- 2.39.5