Many sources present the Euler, Verlet, velocity Verlet, and leapfrog algorithms for integrating Newton's equations.  Based on the order of accuracy, it is agreed that velocity Verlet, Verlet, and leapfrog are superior to the Euler method.  It can also be shown that the Verlet and velocity methods are algebraically equivalent.  What are the advantages and disadvantages of using velocity Verlet or leapfrog integrators?  Is one more accurate or expensive than the other?
Comparison of velocity Verlet and leapfrog algorithms
ode;time integration