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I was wondering what the difference is between the Størmer Verlet method and the regular Verlet method, if there is any.

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My impression is that the two methods are the same, in both cases the position is updated using $$x_{n+1}=2x_n-x_{n-1}+a_n\Delta t^2$$ with $a_n$ the acceleration.

Usually, however, I hear "Verlet integration" to be about the velocity Verlet method, where the velocity at the half-step is used:

  1. Compute $x(t+\Delta t)=v(t)+\frac12a(t)\Delta t^2$
  2. Compute $a(t+\Delta t)$ using the updated position
  3. Compute $v(t+\Delta t)=v(t)+\frac12\left(a(t)+a(t+\Delta t)\right)\Delta t$

This, of course, assumes the acceleration does not depends on velocity, which would require a slight modification to the algorithm (I discuss this here). The link Qmechanic's added to your post can provide more details to the base method.

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  • $\begingroup$ The method was rediscovered several times, including by Störmer, and by Verlet. Sometimes it is called Newton-Störmer-Verlet, because it appeared in Newton's Principia Mathematica. Some of the historical background can be found here also doi:10.1017/S0962492902000144. $\endgroup$ – user197851 Dec 13 '18 at 13:13
  • $\begingroup$ @LonelyProf yes, that is my understanding. In fact, the Wikipedia entry on Stormer says that he used the Verlet method for a problem and that's why it's also called the Stormer method. $\endgroup$ – Kyle Kanos Dec 13 '18 at 13:15
  • $\begingroup$ And my apologies for mis-spelling Størmer, too late to correct now.... $\endgroup$ – user197851 Dec 13 '18 at 13:19
  • $\begingroup$ @LonelyProf I can't even get it on my cellphone keyboard, so I'm totally okay ;)... curiously, the guy's name uses a "slashed o" whereas the method uses an "umlaut o". $\endgroup$ – Kyle Kanos Dec 13 '18 at 13:22

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