Schematic of the numerical problem. The (independent) grid parameter m ranges from the core mass M_core to the (unknown) total mass M. The five structure equations for P, T, r, M_z, and E are solved byimposing ten boundary conditions. The radii R_core and R_out follow from M_core and M, respectively, and M_Z,tot is incremented according to the time-step Δt, ΔM_Z,tot = Ṁ_pebΔt. The total energy E is needed to provide the luminosity L at any point (Eq. (10)). In Phase II, M_core becomes a known parameter, while the metallicity threshold parameter Z_max is added as an unknown.