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We describe and discuss the properties of three numerical methods for solvingthe diffusion equation for the transport of the chemical species and of theangular momentum in stellar interiors. We study through numerical experimentsboth their accuracy and their ability to provide physical solutions. On thebasis of new tests and analyses applied to the stellar astrophysical context,we show that the most robust method to follow the secular evolution is theimplicit finite differences method. The importance of correctly estimating thediffusion coefficient between mesh points is emphasized and a procedure forestimating the average diffusion coefficient between a convective and aradiative zone is described.Comment: 15 pages, 8 figures. accepted for publication in Astronomy and  Astrophysic

Diffusion in stellar interiors: Critical tests of three numerical methods