ABSTRACT
The structure of a star is determined by the interaction of a number of basic physical processes, including nuclear fusion; energy transport by radiation, convection, and conduction; atomic physics involving, especially, the interaction of radiation with matter; and the equation of state and thermodynamics of a gas. These principles, combined with basic equilibrium relations and assumed mass and chemical composition, allow the construction of mathematical models of stars. During the pre-main-sequence phase, the structure evolves as a result of gravitational contraction and the resulting heating of the interior. On the main sequence, evolution is driven by the change in chemical composition, specifically the conversion of hydrogen to helium as a result of nuclear reactions. During the post-main-sequence phase, the evolution is driven by a combination of nuclear transformations as well as contraction and expansion of various layers of the star. To follow this evolution mathematically requires the solution of a complicated set of equations. Even though a star can, to a high degree of approximation, be regarded as a sphere, so that the equations can be set up in one space dimension, the time-dependent solution is complicated enough so that numerical methods are required. The goal of the calculations is to obtain a complete evolutionary history of a star, as a function of its initial mass and chemical composi-
tion, from its birth in an interstellar cloud to its final state as a compact remnant, and to predict the observable properties of the object as a function of time. This chapter discusses the equations that are to be solved, the numerical method most commonly used to solve them, and the physics that must be included in the calculation.
