  A clear understanding of the mechanisms that control the electron dynamics in
strong laser field is still a challenge that requires to be interpreted by
advanced theory. Development of accurate theoretical and computational methods,
able to provide a precise treatment of the fundamental processes generated in
the strong field regime, is therefore crucial. A central aspect is the choice
of the basis for the wave-function expansion. Accuracy in describing
multiphoton processes is strictly related to the intrinsic properties of the
basis, such as numerical convergence, computational cost, and representation of
the continuum. By explicitly solving the 1D and 3D time-dependent Schr\"odinger
equation for H$^{+}_{2}$ in presence of an intense electric field, we explore
the numerical performance of using a real-space grid, a B-spline basis, and a
Gaussian basis (improved by optimal Gaussian functions for the continuum). We
analyze the performance of the three bases for high-harmonic generation and
above-threshold ionization for H$^{+}_{2}$. In particular, for high-harmonic
generation, the capability of the basis to reproduce the two-center
interference and the hyper-Raman phenomena is investigated.
