$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
What to learn in the start-up example; mathematical analysis
- How to uncover numerical artifacts in the computed solution
- How to analyze the numerical schemes mathematically to understand
why artifacts occur
- How to derive mathematical expressions for various measures of
the error in numerical methods, frequently by using the
sympy software
for symbolic computation
- Introduce concepts such as finite difference operators,
mesh (grid), mesh functions,
stability, truncation error, consistency, and convergence
