STATEMENT OF THE PROBLEM OF GRAVITATIONAL COLLAPSE OF A STELLAR IRON-OXYGEN CORE AND A NUMERICAL-METHOD OF ITS SOLUTION

We present a method of integrating the transfer equations for neutrino s of different sorts together with the solution of the hydrodynamic eq uations for matter and the kinetic equations that describe one-dimensi onal gravitational collapse of stellar cores. The method is based on t he replacement of the derivatives with respect to the neutrino coordin ate, angle, and energy by finite differences and on the solution of th e resulting system of ordinary differential equations by Gear's method tan implicit method of a high order of accuracy). The difference equa tions are written so that they approximate the differential equations in an optically thick region by central differences with the second or der of accuracy to correctly change to the equations of neutrino therm al conductivity and by upwind differences of the first order of accura cy in an optically thin region to eliminate the false oscillations in the numerical solution. Because of the stability of Gear's method in s olving rigorous systems of ordinary differential equations (ODEs), the numerical calculations can be performed with large time steps, withou t specially separating the region with neutrino thermal conductivity, and the kinetics of nuclear reactions can also be readily taken into c onsideration.