Evolution of Single Stars III. Stationary Shell Sources

A detailed description is given of the numerical technique used to follow the evolution of stellar models with a very thin shell source (or shell sources). The shell source region is assumed to be almost stationary and the time derivatives of all the physical quantities are replaced with their space derivatives multiplied by the rate of mass flow. As a result the structure of the shell source is described by the ordinary differential equations and it is possible to include in the envelope integrations. Such deep envelope integrations may be used to calculate the outer boundary conditions for the stellar core. The evolution of the helium core up to the helium flash, and the evolution of the carbon-oxygen core up to the carbon flash was followed in this manner. It is suggested that the radius r may be used instead of the mass fraction M_r as an independent space variable in the Henyey-type programs if one does not like to put the shell source in the envelope.