Symplectic integrators: An introduction

Symplectic integrators very nearly conserve the total energy and are particularly useful when treating long times. We demonstrate some of the properties of these integrators by exploring the structure of first-, second-, and fourth-order symplectic integrators and apply them to the simple harmonic oscillator. We consider numeric, geometric, and analytic aspects of the integrators with particular attention to the computed energies. (c) 2005 American Association of Physics Teachers.