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It is becoming increasingly important to analyze the static and dynamic characteristics of flying head sliders over discrete track media (DTM) and bit patterned media (BPM) using the molecular gas-film lubrication (MGL) equation. In this study, we obtained the dynamic characteristics of the air bearing of the read/write head by considering not only the stiffness and damping produced by the air film, but also the negative stiffness caused by the attractive van der Waals force; these quantities were calculated in the frequency domain using a perturbation method. The dependence of the dynamic characteristics on the groove depth and frequency were calculated numerically. Moreover, the cubic interpolated propagation (CIP) method, a highly accurate and numerically stable scheme, was extended to the two-dimensional MGL problem in the time domain and the time evolution of the pressure produced by a single projection on the running disk, which is the simplest configuration of BPM, was calculated numerically.