Ordinary Differential Equations

$${du \over dt} = f(u,t) \hbox{ approximated using } t^n \equiv t^0 + n\Delta t, \ u^n \equiv u(t^n), \ f^n \equiv f(u^n,t^n)$$

$$\begin{tabular} {\vert c\vert c\vert c\vert c\vert} \hline\h... ...s\\ --- \\ A-stable \end{tabular}\\ \hline\hline\end{tabular}$$

$$\begin{tabular} {\vert c\vert c\vert c\vert c\vert} \hline\h... ...O(\Delta t^4)\end{array}$& yes& yes\\ \hline\hline\end{tabular}$$

$$\begin{tabular} {\vert c\vert c\vert c\vert c\vert} \hline\h... ...n+1}f^{\nv}+O(\Delta t^2)$& no& yes\\ \hline\hline\end{tabular}$$