Convection Equation

$${\partial u \over \partial t} + a {\partial u \over \partial x} = f(x,t)$$

$$t^n \equiv t^0 + n\Delta t\quad x_j \equiv x_0 + j\Delta x\quad u^n_j \equiv u(x_j,t^n) \quad f^n_j \equiv f(x_j,t^n)$$

$$C \equiv {a \Delta t\over \Delta x}$$

$$\begin{tabular} {\vert c\vert c\vert c\vert} \hline\hline \m... ... C\le 2$.\end{center}}\end{tabular}\\ \hline\hline\end{tabular}$$

$$\begin{tabular} {\vert c\vert c\vert c\vert} \hline\hline \m... ...e 1$.\end{center}} \\ \end{tabular}\\ \hline\hline\end{tabular}$$

$$\begin{tabular} {\vert c\vert c\vert c\vert} \hline\hline \m... ...\ Stable. \\ Accurate.\end{tabular}\\ \hline\hline\end{tabular}$$

$$\begin{tabular} {\vert c\vert c\vert c\vert} \hline\hline \m... ...\ Implicit. \\ Stable.\end{tabular}\\ \hline\hline\end{tabular}$$