Some robust integrators for large time dynamics

Some robust integrators for large time dynamics

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 con...

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Bibliographic Details
Main Authors: Dina Razafindralandy, Vladimir Salnikov, Aziz Hamdouni, Ahmad Deeb
Format: Article
Language:English
Published: SpringerOpen 2019-03-01
Series:Advanced Modeling and Simulation in Engineering Sciences
Subjects:
Symplectic integrators
Dirac integrators
Long-time stability
Borel summation
Divergent series
Online Access:http://link.springer.com/article/10.1186/s40323-019-0130-2
Description
Summary: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.
ISSN:2213-7467

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