The dynamics of the diffusive-thermal oscillations of flame stabilized at the surface of a porous flat burner is investigated in the current study by using both experimental and computational approaches. The quantitative experimental data for the neutral stability boundary and for the properties of the pulsating solutions of a methane/air system at ambient conditions is presented. The time resolved distribution of OH radicals in the unsteady pulsating combustion front at different heights above the burner is measured and reported for the first time for such a configuration and combustion regime. In order to obtain quantitative numerical results, well known and established mechanisms of methane oxidation: GRI, San-Diego and Warnatz, together with a mixture averaged diffusion model (with the Soret thermo-diffusion included) are employed in the computational study. The numerical results are compared to the experimental results, collected through the chemiluminescence and Laser-Induced Fluorescence (LIF) of the hydroxyl radical. All three mechanisms tested in the current work give quantitatively different values of the neutral stability, frequency and amplitude of the oscillations for the same values of parameters, though all computed and measured results qualitatively agree. A very rich dynamic behaviour is reported ranging from ordinary flame oscillations regimes near the burner surface to a periodic sequence of ignition near the surface of the burner and transition to extinction far downstream. We demonstrate that the characteristics of pulsating regimes are very sensitive to the choice of reaction mechanisms. The variety and complexity of dynamical regimes reported as well as success in measuring and computing the phenomenon with high accuracy open perspectives for additional verification of reaction mechanisms.