From an oversimplified perspective, I reckon Euler and Verlet and Leapfrog integration are quite basic and quite similar. Euler is the simplest imaginable scheme (ignoring fine math insights) of step by step calculations of position, velocity, acceleration.<p>Leapfrog is the same process as Euler integration, except the velocity values are initially nudged to set their state to the middle of the update timestep so that when the timestep is applied from t to t+1, the velocity applied is middle/average of that step (at t+0.5)<p>Verlet integration noted by this project, seems to be essentially Leapfrog integration, while not storing velocity data explicitly-separately from position information.<p>From a programming perspective, these seem to be very basic and similar integration schemes which can be overcomplicated by mathematical descriptions. I have programmed and used leapfrog basically. The Rebound engine includes some tasty looking advanced integration schemes where the fine math seems more necessary to grasp what is being calculated.