A FAMILY OF SYMPLECTIC INTEGRATORS: STABILITY, ACCURACY, AND MOLECULAR DYNAMICS APPLICATIONS

The following integration methods for special second-order ordinary differential equations are studied: leapfrog, implicit midpoint, trapezoid, Störmer-Verlet, and Cowell-Numerov. We show that all are members or or equivalent to members, of one-parameter family of schemes. Some methods have more than one common form, and we discuss a systematic enumeration of these forms. We also present a stability and accuracy analysis based on the idea of "modified equations" and a proof  of symplecticness. It follows  that Cowell-Numerov and "LIM2" (a method proposed by Zhang and Schlick) are symplectic.  A different interpretation of the values used by these integrators leads to higher accuracy and better energy conservation. Hence we suggest that the straightforward analysis of energy conservation is misleading.

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