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High accuracy splitting algorithms based on the unitary approximations of the evolution operator for the timedependent Schrödinger equation (TDSE) with a train of laser pulses are developed. The efficiency of the algorithms is shown using typical examples of a hydrogen atom affected by a train of laser pulses in the dipole approximation and an additional constant magnetic field. The stabilization effects are discussed.doi:10.1117/12.578913 fatcat:u3kz6jyyyfe3ppnjo7txv7inzi