Photoinduced quantum molecular dynamics is numerically investigated using two different Schrödinger formulations based on adiabatic ("bare") and Floquet ("dressed") molecular state representations. Computer simulations for the two approaches are compared in terms of numerical accuracy and efficiency where special emphasis is laid on the limit of very short and intense laser pulses. The optical excitation of the HCl⁺ ion from the X ²Π to the A ²Σ⁺ state near resonance frequency is investigated as a model system. For a variety of pulse intensities and durations the final population transfer is reproduced accurately by a model based on seven Floquet states only. Elimination of the highly oscillatory terms from the resulting equations allows for the use of much longer time steps in the numerical integration. Even for extremely short pulses with durations down to a single optical cycle, dressed states are still found to be useful. Thus, the Floquet approach provides an efficient tool for the simulation of molecules interacting with short and intense pulses beyond the perturbative regime.