Numerical solution technique for the transient equation of transfer

The present investigation is concerned with a class of problems in which the process of scattering radiation is governed by a partial integrodifferential equation, taking into account the search for a numerical solution. A finite-difference method is developed for the solution of the transient equation of transfer in a plane parallel medium. It is shown that a finite-difference form of the governing equation is identical to that of the stationary or time-independent equation of transfer. If the boundary conditions and source function are finite and continuous, this equation may be solved at discrete values of the transient variable. The adding/doubling method is used for the solution of the equation of transfer. The considered approach provides solutions to a number of problems for radiative transfer or neutron transport applications. Two cases are investigated.