Abstract
A fourth-order three-stage symplectic integrator similar to the second-order Störmer—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 Störmer—Verlet-like scheme has a larger numerical stable zone than either the Störmer—Verlet method or the fourth-order Forest—Ruth symplectic algorithm, and its numerical errors in the discrete Hamiltonian and numerical solution are also smaller.
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