Velocity-Verlet Algorithm Sample Clauses

Velocity-Verlet Algorithm. ‌ To evaluate the integration precision, a Xxxxxx’x expansion is performed to the position vector →r. This however, involves large errors and is only accurate to O(∆t). 2m F→ (t) 3! dt3 t=t  →r(t − ∆t) = →r(t) − →v(t)∆t + →r(t + ∆t) = →r(t) + →v(t)∆t + F→ (t) ∆t2 + 1 d3→r | ∆t3 + O(∆t4) 3! dt3 2m ∆t2 − 1 d →r |t=t∆t3 + O(∆t4) Verlet integration minimises the accumulation of error during the MD simulation by summing up the above two equations so that both the velocity term and third-order terms cancel out in numerical computations. The resulting →r(t + ∆t) is accurate to ∼ O(∆t4) (Eq.2.33). − →r(t + ∆t) = 2→r(t) + →r(t ∆t) + F→ ∆t2 + O(∆t4) (2.33) m