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In this paper we generalized the fast convergent Forth-and-Back Implicit   Lambda Iteration (FBILI) method to the solution of the two-level atom line   transfer problems in media with low velocity fields using the observer’s   reference frame. In order to test the accuracy and the convergence properties   of the method we solved several astrophysically important benchmark problems   of the NLTE line formation: in a plan-parallel differentially expanding   medium of finite thickness, and in spherically symmetric stellar atmospheres,   both static and expanding. We compared our solutions with those obtained by   other authors using different numerical methods. [Projekat Ministarstva nauke   Republike Srbije, br. 176004: Stellar Physics

FBILI method for the two-level atom line formation in media with low velocity fields