Application of the Stormer-Verlet-Like Symplectic Method to the Wave Equation

A fourth-order three-stage symplectic integrator similar to the second-order St(o|¨)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(o|¨)rmer-Verlet-like scheme has a larger numerical stable zone than either the St(o|¨)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.