From abaf439b27cf19fc1b539524f8715794109809ad Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?V=C3=ADctor?= Date: Sat, 13 Jan 2024 19:21:22 +0100 Subject: [PATCH] removed double a typo --- .../Numerical_integration_of_partial_differential_equations.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Numerical_integration_of_partial_differential_equations.tex b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Numerical_integration_of_partial_differential_equations.tex index 7dcf227..9d7138d 100644 --- a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Numerical_integration_of_partial_differential_equations.tex +++ b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Numerical_integration_of_partial_differential_equations.tex @@ -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}