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
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.