Convergence of the time-discretized monotonic schemes
Many numerical simulations in (bilinear) quantum control use the monotonically convergent Krotov algorithms (introduced by Tannor [ (1992) 347–360]), Zhu and Rabitz [ (1998) 385–391] or their unified form described in Maday and Turinici [ (2003) 8191–8196]. In Maday [ (2006) 323–338], a time discretization which preserves the property of monotonicity has been presented. This paper introduces a proof of the convergence of these schemes and some results regarding their rate of convergence.