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removed double a typo
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victorballester7 committed Jan 13, 2024
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Expand Up @@ -111,7 +111,7 @@
& ={(\abs{\alpha}+\abs{\beta})}^2 \sum_{m\in\ZZ}\norm{\vf{v}_{m}^n}^2 \\
& \leq{(\abs{\alpha}+\abs{\beta})}^{2(n+1)} \sum_{m\in\ZZ}\norm{\vf{v}_{m}^0}^2
\end{align*}
\end{sproof}aa
\end{sproof}
\begin{theorem}[Courant-Friedrichs-Lewy condition]
Consider the traffic equation $$\vf{u}_t+\vf{A}\vf{u}_x=0$$ with $\vf{A}\in\mathcal{M}_q(\RR)$ and a finite difference scheme of the form $$\vf{v}_m^{n+1}=\alpha \vf{v}_{m-1}^n+\beta \vf{v}_m^n+\gamma \vf{v}_{m+1}^n$$ with $k/h=\lambda=\const$ Then, if the scheme is convergent, we have $\abs{a_i\lambda}\leq 1$ $\forall a_i\in\sigma(\vf{A})$.
\end{theorem}
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