The error on the first time step then is of order O ( Δ Δ t 3 ) . This is not considered a problem because on a simulation over a large number of time steps, the error on the first time step is only a negligibly small amount of the total error, which at time t n is of the order O ( e L t n Δ Δ t 2 ) , both for the distance of the position vectors x n to x ( t n ) as for the distance of the divided differences x n + 1 − − x n Δ Δ t to x ( t n + 1 ) − − x ( t n ) Δ Δ t . Moreover, to obtain this second-order global error, the initial error needs to be of at least third order.