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Symplectic integrators for Hamiltonian problems: An overview. (English) Zbl 0762.65043

Acta Numerica 1992, 243-286 (1992).
[For the entire collection see Zbl 0745.00007.]
The author studies the notion of symplecticness and defines the notion of the symplectic integrator. Symplectic integrators fall into two categories: 1) standard methods (as Runge-Kutta or Runge-Kutta-Nyström methods) and 2) methods derived via so-called generating functions.
The second type of symplectic integrators and the generating functions are at the root of the Hamilton-Jacobi method for integrating differential systems via Hamilton-Jacobi partial differential equations.
The author studies these two categories of symplectic integrators with the goal of seeing them in the light of the Hamilton-Jacobi theory.
Reviewer: L.-I.Anita (Iaşi)

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Citations:

Zbl 0745.00007
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