  We present an ab initio approach to solve the time-dependent Schr\"odinger
equation to treat electron and photon impact multiple ionization of atoms or
molecules. It combines the already known time scaled coordinate method with a
new high order time propagator based on a predictor-corrector scheme. In order
to exploit in an optimal way the main advantage of the time scaled coordinate
method namely that the scaled wave packet stays confined and evolves smoothly
towards a stationary state the modulus square of which being directly
proportional to the electron energy spectra in each ionization channel, we show
that the scaled bound states should be subtracted from the total scaled wave
packet. In addition, our detailed investigations suggest that multi-resolution
techniques like for instance, wavelets are the most appropriate ones to
represent spatially the scaled wave packet. The approach is illustrated in the
case of the interaction of an one-dimensional model atom as well as atomic
hydrogen with a strong oscillating field.
