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The study of AGB stars necessarily covers a wide range of topics, from the primary astronomical observations to their interpretation in terms of fundamental physics. All that requires proper ad hoc methodologies, among which numerical modeling of the outer layers of AGB stars plays a paramount role. In this paper, we present an iterative sequential procedure, operative and physically sound, tailored to compute extended stellar atmospheres. It will constitute the backbone of the in fieri TEIDE package to be implemented into our VULCAN code. Such an improvement will allow us to compute more realistic models of the extended atmospheres of AGB stars taking into account important physical aspects that are neglected in the actual version of VULCAN.

AGB Stars and Their Circumstellar Envelopes: An Operative Approach to Computing Their Atmospheres