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arXiv · 2406.16423

A variational symplectic scheme based on Simpson's quadrature

François Dubois·Juan Antonio Rojas-Quintero
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Abstract

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.

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François Dubois, Juan Antonio Rojas-Quintero. 2024-06-24. A variational symplectic scheme based on Simpson's quadrature. https://arxiv.org/abs/2406.16423

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