Application of the St?rmer–Verlet-Like Symplectic Method to the Wave Equation^*

A fourth-order three-stage symplectic integrator similar to the second-order St?rmer–Verlet method has been proposed and used before Chin. Phys. Lett. 28 (2011) 070201; Eur. Phys. J. Plus 126 (2011) 73. Continuing the work initiated in the publications, we investigate the numerical performance of the integrator applied to a one-dimensional wave equation, which is expressed as a discrete Hamiltonian system with a fourth-order central difference approximation to a second-order partial derivative with respect to the space variable. It is shown that the St?rmer–Verlet-like scheme has a larger numerical stable zone than either the St?rmer–Verlet method or the fourth-order Forest–Ruth symplectic algorithm, and its numerical errors in the discrete Hamiltonian and numerical solution are also smaller.