Table of Contents

Lax Wendroff Stability Analysis

Author: Philip Nelson (see also p.213 of text)

\(g(\xi) = 1 - \frac{1}{2}v(e^{i\xi h} - e^{-i\xi h}) + \frac{1}{2}v^2(e^{i\xi h} - 2 + e^{-i\xi h})\) \(= 1 - iv\sin(\xi h) + v^2(\cos(\xi h) - 1)\) \(= 1 - iv \Big( 2\sin(\frac{\xi h}{2})cos(\frac{\xi h}{2} \Big) + v^2 \Big( 2sin^2(\frac{\xi h}{2}) \Big)\) \( \implies |g(\xi)|^2 = \Big( 1 - 2sin^2(\frac{\xi h}{2}) \Big)^2 + 4\sin^2(\frac{\xi h}{2})cos^2(\frac{\xi h}{2})\) \(= 1 - 4v^2(1 - v^2)sin^4(\frac{\xi h}{2})\) \( \implies \text{stable for } |v| \leq 1\)

Last Modification date: 5 May 2018