Velocity Verlet algorithm

$r(t+\delta t)=r(t)+\delta tv(t)+{\frac {1}{2}}\delta t^{2}a(t)$

$v\left(t+\delta t\right)=v(t)+{\frac {1}{2}}\delta t[a(t)+a(t+\delta t)]$

References

1. Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review 159 pp. 98 - 103 (1967)
2. William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics 76 pp. 637-649 (1982)