Loading [MathJax]/extensions/TeX/boldsymbol.js
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\dfc}{\alpha} % diffusion coefficient
Analysis of the finite difference schemes
Stability:
- |A| < 1 : decaying numerical solutions (as we want)
- A < 0 : oscillating numerical solutions (as we do not want)
Accuracy:
- Compare numerical and exact amplification factor: A vs \Aex = \exp{(-\dfc k^2 \Delta t)}
