Heat Equation

$${\partial u \over \partial t} - \nu {\partial^2 u \over \partial x^2} = f(x,t) \qquad \nu\gt$$

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

$$N \equiv {\nu \Delta t\over \Delta x^2}$$

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

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

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

$$\begin{tabular} {\vert c\vert c\vert c\vert} \hline\hline \m... ...urate. \\ Dissipative.\end{tabular}\\ \hline\hline\end{tabular}$$