Some robust integrators for large time dynamics

2018/11/22 by Dina Razafindralandy, Vladimir Salnikov, Razafindralandy, Dina +5 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · doi:10.48550/arxiv.1811.09114

openalex publication_date 2018/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through numerical examples. Next, Dirac integrators for constrained systems are exposed. An application on chaotic dynamics is presented. Lastly, for systems having no exploitable geometric structure, the Borel-Laplace integrator is presented. Numerical experiments on Hamiltonian and non-Hamiltonian systems are carried out, as well as on a partial differential equation. Keywords: Symplectic integrators, Dirac integrators, long-time stability, Borel summation, divergent series.

Citations

• Exponential Time Differencing for Stiff Systems

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