Efficient time-dependent method for strong-field processes in atoms with smoothly varying radial steps*

We present an efficient numerical method to solve the time-dependent Schr\"{o}dinger equation in the single-active electron picture for atoms interacting with intense optical laser fields. Our approach is based on a non-uniform radial grid with smoothly increasing steps for the electron distance from the residual ion. We study the accuracy and efficiency of the method, as well as its applicability to investigate strong-field ionization phenomena, the process of high-order harmonic generation, and the dynamics of highly-excited \hbox{Rydberg} states