Some robust integrators for large time dynamics
For researchers in numerical simulation of differential equations, this review provides a comparative overview of integrators suitable for long-time integration, but it is incremental as it surveys existing methods without introducing new algorithms or achieving new SOTA results.
This paper reviews symplectic, Dirac, and Borel-Laplace integrators for large-time dynamics, demonstrating stability and accuracy on Hamiltonian and non-Hamiltonian systems, including chaotic dynamics and PDEs, with numerical experiments showing long-time stability.
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.