  We analyze the line radiative transfer in protoplanetary disks using several
approximate methods and a well-tested Accelerated Monte Carlo code. A low-mass
flaring disk model with uniform as well as stratified molecular abundances is
adopted. Radiative transfer in low and high rotational lines of CO, C18O, HCO+,
DCO+, HCN, CS, and H2CO is simulated. The corresponding excitation
temperatures, synthetic spectra, and channel maps are derived and compared to
the results of the Monte Carlo calculations. A simple scheme that describes the
conditions of the line excitation for a chosen molecular transition is
elaborated. We find that the simple LTE approach can safely be applied for the
low molecular transitions only, while it significantly overestimates the
intensities of the upper lines. In contrast, the Full Escape Probability (FEP)
approximation can safely be used for the upper transitions ($J_{\rm up} \ga 3$)
but it is not appropriate for the lowest transitions because of the maser
effect. In general, the molecular lines in protoplanetary disks are partly
subthermally excited and require more sophisticated approximate line radiative
transfer methods. We analyze a number of approximate methods, namely, LVG, VEP
(Vertical Escape Probability) and VOR (Vertical One Ray) and discuss their
algorithms in detail. In addition, two modifications to the canonical Monte
Carlo algorithm that allow a significant speed up of the line radiative
transfer modeling in rotating configurations by a factor of 10--50 are
described.
