AbstractNumerical methods are essential to the treatment of line formation in inhomogeneous non-LTE atmospheres. The new methods due to Hummer and Rybicki and to Feautrier now make it possible to make such calculations, although these are often quite timeconsuming.We shall describe an alternative approach using discrete space techniques depending on concpets of invariance. The solution algorithm is closely related to the method of Hummer and Rybicki, whose equations are obtained as a limiting

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... se. The stability and errors of our algorithm are susceptible to mathematical analysis, and make it possible to identify the critical parameters in the calculation with precision. The results for a two-level problem will be compared with those from an implementation of the Rybicki-Hummer equations and a comparison will be made of the performance of the two procedures in respect of speed of computation and storage requirements.