Staggered Time Integrators for Wave Equations

We consider variations of the Adams--Bashforth, backward differentiation, and Runge--Kutta families of time integrators to solve systems of linear wave equations on uniform, time-staggered grids. These methods are found to have smaller local truncation errors and to allow larger stable time steps than traditional nonstaggered versions of equivalent orders. We investigate the accuracy and stability of these methods analytically, experimentally, and through the use of a novel root portrait technique.