Journal of Applied Mathematics

Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations

Abdallah A. Nahla and Mohammed F. Al-Ghamdi

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 282367, 12 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495141

Digital Object Identifier
doi:10.1155/2012/282367

Mathematical Reviews number (MathSciNet)
MR2923369

Zentralblatt MATH identifier
1252.82128

Citation

Nahla, Abdallah A.; Al-Ghamdi, Mohammed F. Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations. J. Appl. Math. 2012 (2012), Article ID 282367, 12 pages. doi:10.1155/2012/282367. https://projecteuclid.org/euclid.jam/1355495141


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