Stochastic heating is an important phenomenon in low-pressure radio-frequency (RF) capacitive discharges. Recent theoretical work on this problem using several different approaches has produced results that are broadly in agreement in-so-far as scaling with the discharge parameters is concerned, but there remains some disagreement in detail concerning the absolute size of the effect. Here we report a simulation study for single and dual frequency capacitive discharges with two main aims. In the case of single frequency discharge, this work investigates the dependence of stochastic heating on various discharge parameters by scaling of these parameters with the help of particle-in-cell (PIC) simulation. This research work produces a relatively extensive set of simulation data that may be used to validate theories over a wide range of parameters. The analytical models are satisfactory for intermediate current density amplitude ˜ J0 (or control parameter H) and in agreement with PIC results. However in extreme cases new physical effects appear (like field reversal, electron trapping, reflection of ions etc.) and the simulation results deviate from existing analytical models. The dependence of stochastic heating on applied frequency is also investigated. The second aim is to study any evidence of wave emission with a frequency near the electron plasma frequency at the sheath edge. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. These waves are damped during their propagation from the sheath towards the bulk plasma. The damping occurs because of the Landau damping or some related mechanism. This research work reports that the emission of waves is associated with a field reversal during the expansion phase of the sheath. Trapping of electronsnear to this field reversal region is observed. Calculation shows that these waves are electron plasma waves. In the dual frequency case, this research has produced a relatively extensive set of simulation data and shown that the dual-frequency analytical model is in agreement for wide range of parameters. However, in extreme cases, new phenomena like the presence of strong field reversal and the reflection of ions appear and the simulation results deviate from the analytical model. A further aim is the investigation of the presence of strong wave phenomena during the expanding and collapsing phase of the low frequency sheath. The characteristics of waves in the dual-frequency case is entirely different from the single-frequency case. The presence of electron trapping near to the field reversal regions is also observed at multiple times of an RF period. The frequency of these waves are calculated and to be of the order of the plasma frequency.