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Symplectic integrators for Hamiltonian problems: an overview

Published online by Cambridge University Press:  07 November 2008

J. M. Sanz-Serna
J. M. Sanz-Serna
Affiliation:
Departamento de Matemática Aplicada y ComputaciónFacultad de CienciasUniversidad de Valladolid, Valladolid, Spain, E-mail: sanzserna@cpd.uva.es
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Extract

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.

Type
Research Article
Information
Acta Numerica , Volume 1 , January 1992 , pp. 243 - 286
Copyright
Copyright © Cambridge University Press 1992

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