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Fixes bug in theory.md section of docs
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msleigh committed Jan 21, 2024
1 parent 74fe0fb commit 2326c6b
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5 changes: 4 additions & 1 deletion docs/theory.md
Original file line number Diff line number Diff line change
Expand Up @@ -147,7 +147,10 @@ $$

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:

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