Acta Numerica

Research Article

Symplectic integrators for Hamiltonian problems: an overview

J. M. Sanz-Sernaa1

a1 Departamento de Matemática Aplicada y Computación Facultad de Ciencias Universidad de Valladolid, Valladolid, Spain, E-mail:

In the sciences, situations where dissipation is not significant may invariably be modelled by Hamiltonian systems of ordinary, or partial, differential equations. Symplectic integrators are numerical methods specifically aimed at advancing in time the solution of Hamiltonian systems. Roughly speaking, ‘symplecticness’ is a characteristic property possessed by the solutions of Hamiltonian problems. A numerical method is called symplectic if, when applied to Hamiltonian problems, it generates numerical solutions which inherit the property of symplecticness.