Statement of the problem of gravitational collapse of a stellar ironoxygen core and a numerical method of its solution
Abstract
We present a method of integrating the transfer equations for neutrinos of different sorts together with the solution of the hydrodynamic equations for matter and the kinetic equations that describe onedimensional gravitational collapse of stellar cores. The method is based on the replacement of the derivatives with respect to the neutrino coordinate, angle, and energy by finite differences and on the solution of the resulting system of ordinary differential equations by Gear's method (an implicit method of a high order of accuracy). The difference equations are written so that they approximate the differential equations in an optically thick region by central differences with the second order of accuracy to correctly change to the equations of neutrino thermal conductivity and by upwind differences of the first order of accuracy in an optically thin region to eliminate the false oscillations in the numerical solution. Because of the stability of Gear's method in solving rigorous systems of ordinary differential equations (ODEs), the numerical calculations can be performed with large time steps, without specially separating the region with neutrino thermal conductivity, and the kinetics of nuclear reactions can also be readily taken into consideration.
 Publication:

Astronomy Letters
 Pub Date:
 July 1998
 Bibcode:
 1998AstL...24..482A