The thesis is focused on the extension of existing techniques as well as the use of cutting-edge parallelisation in the development of methods for quantum systems in intense ultra-short laser fields. The calculations for the quantum systems are performed fully ab initio; using as few approximations as possible. Among the popular approaches for ab initio calculations are those which use an energy eigenstate basis and those which handle the wavefunction explicitly on a grid. In this thesis these methods are both used for considering hydrogen and the molecular hydrogen ion in intense ultra-short laser fields. The thesis develops on the TDRM approach that simultaneously uses both methods but in a divided configuration space. We develop the approach further by extending the treatment to the H+ system in intense laser 2fields. For this thesis the author has developed a new framework, called CLTDSE, and released it as the first 1 laser-matter Time-dependent Schrodinger Equation (TDSE) code which has been explicitly developed with Graphical Processing units (GPUs) and other parallel architectures at the focus. Although the author’s existing public code release consists of finite difference methods, the current code provides support for the finite difference and basis methods, TDRM as well as general Ordinary Differential Equation (ODE) problems. It also performs the B-spline based diag- onalisation for hydrogenic systems and the calculation of the dipole moment and dipole acceleration. By using OpenCL automatic support for multi-core Central Processing Units (CPUs) has also been provided. We discuss the parallelisation strategy in the thesis and the performance of a variety of methods are compared on CPUs and GPUs. It will be seen that a given GPU accelerator is not always a better option than the CPU. Further, it will be shown that large run-time reductions are available when comparing high-end CPUs against high-end GPUs, thus the performance promises of GPU systems are realisable. We further utilise the computational advantages offered by the acceleration by looking at and directly computing the effect of stochastic pulses on atomic hydrogen, with some focus on the effect on ATI structure. The method of calculation used consists of the instantiation of a particular instance of a stochastic pulse and the direct calculation of the resulting yield or other properties of interest.