抄録
In this paper we study the three-dimensional nodal discrete-ordinates approximations of neutron transport equation in a convex domain with piecewise smooth boundaries. We use the combined collocation method of the angular variables and nodal approach for the spatial variables^1. By nodal approach we mean the iterated transverse integration of the S_N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS_N method, first applying the Laplace transform to the set of the nodal S_N equations and then obtaining the solution by symbolic computation. We include the LTS_N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS_N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation^<(2,3)> We give numerical results obtained with an algebraic computer system (for N up to 8) and with a code for higher values of N. We compare our results for the geometry of a box with a source in a vertex and a leakage zone in the opposite vertex with others techniques used in this problem. code for higher values of N. We compare our results for the geometry of a box with a source in a vertex and a leakage zone in the opposite vertex with others techniques used in this problem.
