Extrapolated gradientlike algorithms for molecular dynamics and celestial mechanics simulations

A class of symplectic algorithms is introduced to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an advanced gradientlike decomposition approach. Its main advantage over the standard gradient scheme is the avoidance of time-consuming evaluations of force gradients by force extrapolation without any loss of precision. As a result, the efficiency of the integration improves significantly. The algorithms obtained are analyzed and optimized using an error-function theory. The best among them are tested in actual molecular dynamics and celestial mechanics simulations for comparison with well-known nongradient and gradient algorithms such as the Störmer-Verlet, Runge-Kutta, Cowell-Numerov, Forest-Ruth, Suzuki-Chin, and others. It is demonstrated that for moderate and high accuracy, the extrapolated algorithms should be considered as the most efficient for the integration of motion in molecular dynamics simulations.