WIP backup for Sonoma upgrade

.gitignore

@@ -9,3 +9,4 @@
 docs/html
 docs/latex
 docs/doxygen.log
+.venv

docs/Doxyfile

@@ -1859,7 +1859,7 @@ LATEX_OUTPUT           = latex
 # the output language.
 # This tag requires that the tag GENERATE_LATEX is set to YES.
 
-LATEX_CMD_NAME         = latex
+LATEX_CMD_NAME         = pdflatex
 
 # The MAKEINDEX_CMD_NAME tag can be used to specify the command name to generate
 # index for LaTeX.

docs/theory.md

@@ -147,35 +147,27 @@ $$
 
 is rearranged to give:
 
-$$
-u_r^{n+1} \approx
-\left[ \frac{1-\left(1-\alpha\right)\hat\beta c\Delta t\hat\sigma}{1+\alpha\hat\beta c\Delta t\hat\sigma} \right] u^n_r
-+
-\left[ \frac{\hat\beta\hat\sigma\Delta t}{1+\alpha\hat\beta c\Delta t\hat\sigma} \right] \phi^\lambda
-$$
+$$ u_r^{n+1} \approx \left[ \frac{1-\left(1-\alpha\right)\hat\beta c\Delta t\hat\sigma}{1+\alpha\hat\beta c\Delta t\hat\sigma} \right] u^n_r + \left[ \frac{\hat\beta\hat\sigma\Delta t}{1+\alpha\hat\beta c\Delta t\hat\sigma} \right] \phi^\lambda $$
 
 which allows us to write:
 
 $$ \alpha u^{n+1}_r + \left(1-\alpha\right) u^n_r =
-\frac{\alpha\hat\beta\hat\sigma\Delta t}{1 + \alpha\hat\beta c\Delta t\hat\sigma} \phi^\lambda
-+
+\frac{\alpha\hat\beta\hat\sigma\Delta t}{1 + \alpha\hat\beta c\Delta t\hat\sigma} \phi^\lambda +
 \frac{1}{1 + \alpha\hat\beta c\Delta t\hat\sigma} u^n_r
 $$
 
 Substituting this into the transport equation gives:
 
 $$ \frac{1}{c} \frac{\partial I}{\partial t} + \mu \frac{\partial I}{\partial x} + \sigma I
 = \frac{1}{2}\sigma
-    \left[ \frac{\alpha\hat\beta c\hat\sigma\Delta t}{1 + \alpha\hat\beta c\Delta t\hat\sigma} \phi^\lambda
-+
+    \left[ \frac{\alpha\hat\beta c\hat\sigma\Delta t}{1 + \alpha\hat\beta c\Delta t\hat\sigma} \phi^\lambda +
 \frac{c}{1 + \alpha\hat\beta c\Delta t\hat\sigma} u^n_r\right]
 $$
 
 which we can re-write as:
 
 $$ \frac{1}{c} \frac{\partial I}{\partial t} + \mu \frac{\partial I}{\partial x} + \sigma I =
-\frac{1}{2} \sigma_s \phi^\lambda
-+
+\frac{1}{2} \sigma_s \phi^\lambda +
 \frac{1}{2} c\sigma_a u^n_r
 $$