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...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.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11173012 and 11178002.
文摘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.
