CESAM: A code for stellar evolution calculations

The code CESAM is a consistent set of programs and routines which performs calculations of 1D quasi-static stellar evolution including diffusion and rotation. The principal new feature is the solution of the quasi-static equilibrium by collocation method based on piecewise polynomials approximations projected on their B-spline basis; that allows stable and robust calculations and the exact restitution of the solution not only at grid points. Another advantage is the monitoring by only one parameter of the accuracy and its improvement by superconvergence. An automatic mesh refinement has been designed for adjusting the localizations of grid points according to the changes of unknowns, each limit between a radiative and a convective zones being shifted to the closest grid point. For standard models, the evolution of the chemical composition is solved by stiffly stable schemes of orders up to four; for non-standard models the solution of the diffusion equation employs the Petrov-Galerkin scheme, with the mixing of chemicals in convective zones performed by strong turbulent diffusion. A precise restoration of the atmosphere is allowed for. CESAM computes evolution of stars from the pre-main sequence to the beginning of the He-4 burning 3 alpha cycle. In this paper a detailed description of the algorithms is presented.