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Abstract

In this thesis, the coordinate scaling method, previously developed for the numerical solution of the time-dependent Schrodinger equation, is generalized for the numerical treatment of the time-dependent Dirac equation (TDDE) and has been applied for the atomic ionization problem in relativistically strong laser fields. To enable the use of the scaling method in relativistic settings, the Foldy-Wouthuysen (FW) transformation is employed within the quasiclassical approximation, reducing TDDE to the square root Klein-Gordon-like equation. The method has been tested on the example of a 1D problem of the 1D atom exposed to a laser field, demonstrating its computational advantage over the standard direct implementation of the TDDE solution, especially in the case of an applied non-uniform mesh. Next, the method in the 2D form has been applied to investigate the strong field ionization of an atom in a XUV laser field in the stabilization regime in the nondipole domain. The pulse duration effect leading to the periodic modulation of the ionization yield has been revealed with the numerical solution and intuitive explanations have been advanced in both dipole and nondipole cases.