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<p>This paper investigates the effectiveness of six kinds of numerical algorithms when applied to two classes of nonlinear dynamical equations, whose nonlinear terms are represented by power functions and trigonometric functions, respectively. The discrete formulations of each numerical integrator for both types of systems are presented in detail. Using these methods, we conduct a comparative analysis of position, velocity, phase space trajectories, energy error, and computational efficiency for two nonlinear systems. The results demonstrate the advantages of geometric numerical integrators in accurately and efficiently solving nonlinear dynamical systems.</p>

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A comparative evaluation of structure-preserving integrators based on the duffing oscillator and coupled pendulums

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Yuanyuan Li,
  • Ben Niu,
  • Shixing Liu,
  • Yongxin Guo

摘要

This paper investigates the effectiveness of six kinds of numerical algorithms when applied to two classes of nonlinear dynamical equations, whose nonlinear terms are represented by power functions and trigonometric functions, respectively. The discrete formulations of each numerical integrator for both types of systems are presented in detail. Using these methods, we conduct a comparative analysis of position, velocity, phase space trajectories, energy error, and computational efficiency for two nonlinear systems. The results demonstrate the advantages of geometric numerical integrators in accurately and efficiently solving nonlinear dynamical systems.