Composition changes during stellar evolution

This paper presents an algorithm by means of which composition changes in stars due to nuclear reactions, convection and semiconvection can be relatively simply calculated. The algorithm is based on a simple physical picture of convective mixing as a diffusion of convective cells throughout a region of a star; however it is not essential to the method that this physical picture be exact. We attempt to show that the method tends, in a limiting sense, to give results which are identical with the `standard' treatment of mixing by convection or semiconvection, for a wide range of possible physical models of convective mixing. The essence of the method is the simultaneous solution, in an implicit difference scheme, of equations governing both the structure and the composition changes in a star. One defect of the method as it was employed here is discussed, and some solutions suggested. Qualitative results are presented for a 14 M main sequence star and a M horizontal branch star.