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In this paper, a two-dimensional mesh-free finite difference scheme is employed to solve the Reynolds equation for IBM3380 slider air bearings. The method derives from weighted least square approximation procedure and a Taylor series expansion of pressure function. To save computation time, the selection of supporting points for each reference node in the computation domain is proposed to be limited in a square area around the reference node in this study. The effect of the weighting functions on the results obtained is also studied. Finally, the numerical difficulty in dealing with the clearance discontinuity is subdued by appropriate node distribution.