Finite difference approximations to time-dependent multigroup transport equations in slab geometry

Abstract

In this article, we consider a monotone iterative scheme to find the solution of a system of finite difference equations approximation to the time-dependent multigroup transport equations in slab geometry. The iterative scheme, coupled with the upper and lower solutions generates two sequences which converge monotonically to the solution of the finite difference equations. It is shown that this monotone convergence leads to the convergence of the solutions of finite difference equations to the solutions of the continuous equations as the mesh length of the space, angle and time variable approaches zero. Numerical results are given for the time-dependent two group transport equations.