In Leapfrog we iterate v <- v + a(x)dt x <- x + vdt With Euler initialisation this is equivalent to: v <- v + a(x)dt/2 x <- x + vdt v <- v + a

In Leapfrog we iterate v <- v + a(x)dt x <- x + vdt With Euler initialisation this is equivalent to: v <- v + a(x)dt/2 x <- x + vdt v <- v + a(x)dt/2 (consider a sequence of steps: we'll have two v <- v + a(x)dt/2 updates next to each other, which gives v <- v + a(x)dt) This is exactly the same as velocity verlet, if you substitute the value for v computed in the first update into the next two equations: x <- x + (v + a(x)dt/2)dt v <- (v + a(x_prev)dt/2) + a(x)dt/2