Sanz-Serna, J. M. 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) Cited in 118 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems Keywords:Hamiltonian system; order conditions; backward error interpretation; KAM theory; symplectic integrator; Runge-Kutta-Nyström methods; generating functions; Hamilton-Jacobi method Citations:Zbl 0745.00007 PDFBibTeX XMLCite \textit{J. M. Sanz-Serna}, Acta Numerica 1992, 243--286 (1992; Zbl 0762.65043)