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An improved Störmer-Verlet method based on exact discretization for nonlinear oscillators

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  • Zhang, Jingjing

Abstract

Motivated by the advantage of exact discretization of a linear differential equation and the importance of symplectic numerical methods for conservative nonlinear oscillators, a modified Störmer-Verlet method relying on a parameter ω is proposed. The main idea is: firstly, based on some analytical approximation strategies, relating a linear equation with the corresponding nonlinear equation such that linear equation’s frequency approximates the exact frequency of the nonlinear equation; secondly, forcing the modified Störmer-Verlet method to solve the related linear equation exactly. The convergence, symplectic and symmetric properties of the new method are analyzed. For numerical implementation, the cubic Duffing equation and the simple pendulum are solved by the new method with some approximate frequencies as the parameter ω, respectively. Numerical results show that the new method is much more accurate than its classical partner.

Suggested Citation

  • Zhang, Jingjing, 2020. "An improved Störmer-Verlet method based on exact discretization for nonlinear oscillators," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304355
    DOI: 10.1016/j.amc.2020.125476
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    References listed on IDEAS

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    1. K. Maleknejad & M. Tamamgar, 2014. "A New Reconstruction of Variational Iteration Method and Its Application to Nonlinear Volterra Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, April.
    2. Tang, Wensheng & Zhang, Jingjing, 2018. "Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 204-219.
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