$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
The steps in the finite difference method
Solving a differential equation by a finite difference method
consists of four steps:
- discretizing the domain,
- fulfilling the equation at discrete time points,
- replacing derivatives by finite differences,
- formulating a recursive algorithm.
