The interactions of low energy He and Ar ions with pure W target were simulated by a new Monte-Carlo (MC) based computer code which was designed to insure maximum accuracy. For these irradiation systems, incident ions projected ranges in the target material, sputtering yield, and the percentage of backscattered ions at various incident energies were studied. furthermore, the effect of the angle of incidence on sputtering yield and the percentage of backscattered ions were also simulated. Our simulation results were compared with experimental data and those calculated by the TRIM simulation program. Our code is based on an algorithm that uses detailed numerical solutions for the classical scattering integral for evaluating the binary collision process. This approach has provided sputtering yield data with a higher level of accuracy compared to TRIM's simulation results. Also, a new approach of using a reduced atomic displacement threshold in the top surface monolayer enhances the simulation results in the near sputtering threshold energy range and eliminates its dependence on the selected value of the displacement energy threshold Ed. Nonetheless, both simulation programs produced less contrasting results in terms of incident ions mean projected ranges. Furthermore, fundamental discrepancies in the percentage of backscattered ions between the results of both simulation programs were found.