International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 16214, 11 pages

Analytical solutions for the neutron transport using the spectral methods

Abdelouahab Kadem

Department of Mathematics, Faculty of Sciences, University of Sétif, Sétif 19000, Algeria

Received 16 May 2005; Revised 27 March 2006; Accepted 4 April 2006

Copyright © 2006 Abdelouahab Kadem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a method for solving the two-dimensional equation of transfer. The method can be extended easily to the general linear transport problem. The used technique allows us to reduce the two-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching for solutions to the multidimensional transport problems leads us to a solution for all values of the independant variables, the proposed method reduces the solution of the multidimensional problems into a set of one-dimensional ones that have well-established deterministic solutions. The procedure is based on the development of the angular flux in truncated series of Chebyshev polynomials which will permit us to transform the two-dimensional problem into a set of one-dimensional problems.