Study guide: Intro to Computing with Finite Difference Methods

Processing math: 100%

$\newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\Aex}{{A_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\Oof}[1]{\mathcal{O}(#1)}$

Summary of stability

Forward Euler is conditionally stable

$\Delta t < 2/a$ for avoiding growth

$\Delta t\leq 1/a$ for avoiding oscillations

The Crank-Nicolson is unconditionally stable wrt growth and conditionally stable wrt oscillations

$\Delta t < 2/a$ for avoiding oscillations

Backward Euler is unconditionally stable