  We introduce Hermite-leapfrog methods for first order wave systems. The new
Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods
of Goodrich and co-authors. The new schemes stagger field variables in both
time and space and are high-order accurate. We provide a detailed description
of the method and demonstrate that the method conserves variable quantities in
one-space dimension. Higher dimensional versions of the method are constructed
via a tensor product construction. Numerical evidence and rigorous analysis in
one space dimension establish stability and high-order convergence. Experiments
demonstrating efficient implementations on a graphics processing unit are also
presented.
