A variational symplectic scheme based on Simpson's quadrature
<|reference_start|>A variational symplectic scheme based on Simpson's quadrature: We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state and we approximate the action in a small time step by the Simpson's quadrature formula. The resulting scheme is explicited for an elementary harmonic oscillator. It is a stable, explicit, and symplectic scheme satisfying the conservation of an approximate energy. Numerical tests illustrate our theoretical study.<|reference_end|>
@article{dubois2024a,
    title={A variational symplectic scheme based on Simpson's quadrature},
    author={Franc{c}ois Dubois (LMO, LMSSC), Juan Antonio Rojas-Quintero},
    journal={Geometric Science of Information, Saint-Malo (France), Aug 2023,
  Saint-Malo, France. pp.22-31},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.16423},
    primaryClass={math.NA cs.NA}
}