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We present an ab initio approach to solve the time-dependent Schr\"odingerequation to treat electron and photon impact multiple ionization of atoms ormolecules. It combines the already known time scaled coordinate method with anew high order time propagator based on a predictor-corrector scheme. In orderto exploit in an optimal way the main advantage of the time scaled coordinatemethod namely that the scaled wave packet stays confined and evolves smoothlytowards a stationary state the modulus square of which being directlyproportional to the electron energy spectra in each ionization channel, we showthat the scaled bound states should be subtracted from the total scaled wavepacket. In addition, our detailed investigations suggest that multi-resolutiontechniques like for instance, wavelets are the most appropriate ones torepresent spatially the scaled wave packet. The approach is illustrated in thecase of the interaction of an one-dimensional model atom as well as atomichydrogen with a strong oscillating field.

Time scaling with efficient time-propagation techniques for atoms and molecules in pulsed radiation fields