1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Need some help with Verlet algorithm

  1. Feb 26, 2008 #1
    1. The problem statement, all variables and given/known data

    I am gonna use the velocity verlet algorithm to simulate the position, velocity and acceleration at time t of some particle.

    2. Relevant equations

    We got the Langevin equation: a(t) = -v(t)/tau - U'(x) / m + F_f(t) / m

    Where tau is the mass divided by the friction coefficient, U'(x(t)) the external force and F_f(t) the fluctuating force. Let's say the external force is harmonic, ½kx(t)^2, so U'(x(t)) / m = kx(t)/m.

    I have so far typed in x(t+dt), v(t+dt/2) and I need to find what a(t+dt) is. It's easier if you go see http://en.wikipedia.org/wiki/Verlet_integration" [Broken] for the equations i refer to :)

    As for a(t+dt) I am in doubt how I should find this, what I tried so far is:

    a(t+dt) = -1/m * dV(x(t+dt))/dx

    = -v(t) / tau - k*x(t+dt) / m + F_f(t)

    (Where I take the value of the fluctuating force randomly from a normaldistribution)

    My doubt is about the use of v(t), can I use v(t) in the above equation? I don't see how many other options I have since we need a(t+dt) to be able to calculate v(t+dt), or have I missed something?

    I hope someone can help me a bit, if you need more info or anything is unclear, please tell me here.
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Feb 27, 2008 #2
    No one able to help? :)
  4. Feb 27, 2008 #3
    The verlet integrator is semi-implicit, which means exactly what you've noticed: you need [tex]v(t+dt)[/tex] to calculate [tex]a(t+dt)[/tex]. In general this means that you need to solve an equation at each step (numerically). Do you have to use Verlet? The usual Runge-Kutta family is pretty good, or even just plain ol' midpoint rule?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook