An improved Störmer-Verlet method based on exact discretization for nonlinear oscillators
作者：
Highlights：
• A modified Störmer-Verlet method with a parameter ω is proposed.
• The modified method is symplectic, symmetric, convergent with order two and explicit for separable Hamiltonian system.
• The modified method solves exactly some linear equation associated to a nonlinear oscillator equation.
• Choosing ω in modified method by approximate frequency of nonlinear oscillator is much more accurate than the classical Störmer-Verlet method.
• Results are verified by numerical experiments on the cubic Duffing and simple pendulum equation.
摘要
•A modified Störmer-Verlet method with a parameter ω is proposed.•The modified method is symplectic, symmetric, convergent with order two and explicit for separable Hamiltonian system.•The modified method solves exactly some linear equation associated to a nonlinear oscillator equation.•Choosing ω in modified method by approximate frequency of nonlinear oscillator is much more accurate than the classical Störmer-Verlet method.•Results are verified by numerical experiments on the cubic Duffing and simple pendulum equation.
论文关键词：Geometric numerical integration,Symplecticity,Exact discretization,Duffing equation,Frequency
论文评审过程：Received 15 July 2019, Revised 13 April 2020, Accepted 14 June 2020, Available online 2 July 2020, Version of Record 2 July 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125476
