Grid staggering for wave equations is a validated approach for many applications, as it generally enhances stability and accuracy. This paper is about time staggering. Our aim is to assess a fourth-order, explicit, time-staggered integration method from the literature, through a comparison with two alternative fourth-order, explicit methods. These are the classical Runge-Kutta method and a symmetric-composition method derived from symplectic Euler.
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Springer
Journal of Scientific Computing
Computational Dynamics

Verwer, J.G. (2007). On time staggering for wave equations. Journal of Scientific Computing, 33(2), 139–154.