# [gmx-users] Velocity Verlet integrator

Mario Fernández Pendás mariofp77 at gmail.com
Wed Oct 15 14:46:37 CEST 2014

Yes, I understand that. But my question is more about why the two velocity
updates are implemented before the position update and not the other way
round?

>From the theoretical point of view I would think more in one of the
following schemes:

1. Calculate: [image: \vec{v}\left(t + \tfrac12\,\Delta t\right) =
\vec{v}(t) + \tfrac12\,\vec{a}(t)\,\Delta t\,]
2. Calculate: [image: \vec{x}(t + \Delta t) = \vec{x}(t) +
\vec{v}\left(t + \tfrac12\,\Delta t\right)\, \Delta t\,]
3. Derive [image: \vec{a}(t + \Delta t)] from the interaction potential
using [image: \vec{x}(t + \Delta t)]
4. Calculate: [image: \vec{v}(t + \Delta t) = \vec{v}\left(t +
\tfrac12\,\Delta t\right) + \tfrac12\,\vec{a}(t + \Delta t)\Delta t,]

1. Calculate: [image: \vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t)\,
\Delta t+\tfrac12 \,\vec{a}(t)\,\Delta t^2]
2. Derive [image: \vec{a}(t + \Delta t)] from the interaction potential
using [image: \vec{x}(t + \Delta t)]
3. Calculate: [image: \vec{v}(t + \Delta t) = \vec{v}(t) +
\tfrac12\,\left(\vec{a}(t)+\vec{a}(t + \Delta t)\right)\Delta t\,]

This is why my confusion arises.

2014-10-15 14:05 GMT+02:00 Justin Lemkul <jalemkul at vt.edu>:

>
>
> On 10/15/14 7:30 AM, Mario Fernández Pendás wrote:
>
>> Dear all,
>>
>> I am still interested in some integrator related issues.
>>
>> I understand that the easiest way to implement velocity Verlet was to
>> split
>> I mean why there are two updates for velocities and then the update for
>> positions?
>> My intuitive idea would be to update first one half for velocities, then a
>> full step for positions and, finally, using these new positions the second
>> half for velocities.
>>
>
> Yes, there are two separate half-step updates for velocities.  The
> comments in the md.cpp code are quite verbose if you want to trace through.
>
> -Justin
>
> --
> ==================================================
>
> Justin A. Lemkul, Ph.D.
> Ruth L. Kirschstein NRSA Postdoctoral Fellow
>
> Department of Pharmaceutical Sciences
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>
> jalemkul at outerbanks.umaryland.edu | (410) 706-7441
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