Abstract and Applied Analysis
Volume 2010 (2010), Article ID 704168, 13 pages
doi:10.1155/2010/704168
Research Article

Note on the Solution of Transport Equation by Tau Method and Walsh Functions

Abdelouahab Kadem1 and Adem Kilicman2

1L.M.F.N Mathematics Department, University of Setif, Setif 19000, Algeria
2Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), Serdang, Selangor 43400, Malaysia

Received 9 November 2010; Accepted 27 December 2010

Academic Editor: Yoshikazu Giga

Copyright © 2010 Abdelouahab Kadem and Adem Kilicman. 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.

Abstract

We consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved that it is a good approximate to exact solutions. This method is based on expansion of the angular flux in a truncated series of Walsh function in the angular variable. The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.