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Journal of Applied Mathematics
Volume 2012, Article ID 282367, 12 pages
http://dx.doi.org/10.1155/2012/282367
Research Article

Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations

1Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2Department of Mathematics, Faculty of Science, Taif University, Taif 888, Saudi Arabia

Received 24 January 2012; Revised 29 February 2012; Accepted 7 March 2012

Academic Editor: Pablo González-Vera

Copyright © 2012 Abdallah A. Nahla and Mohammed F. Al-Ghamdi. 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

Mathematical form for two energy groups of three-dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called “two energy groups of the point kinetics equations.” We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponential model (GAEM) is developed for solving two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix. The eigenvalues of the coefficient matrix are calculated numerically using visual FORTRAN code, based on Laguerre’s method, to calculate the roots of an algebraic equation with real coefficients. The eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the traditional methods. These comparisons substantiate the accuracy of the results of the GAEM. In addition, the GAEM is faster than the traditional methods.