Lax-Wendroff advection scheme ($|\nu |\le 1$)

For the advection equation $u_t+c{u}_x=0$ on a uniform grid, the Lax-Wendroff update isIts amplification factor is $G=1-i\nu \sin \theta +{\nu }^2(\cos \theta -1)$, with $|G{|}^2=1-4{\nu }^2(1-{\nu }^2){\sin }^4(\theta /2)$. Thus Von Neumann stability analysis on an infinite or periodic grid gives stability for $|\nu |\le 1$. The scheme has second order of a numerical method for sufficiently smooth solutions; finite-interval boundary conditions still need separate treatment.