Table of Contents
International Journal of Nuclear Energy
Volume 2013 (2013), Article ID 903904, 12 pages
http://dx.doi.org/10.1155/2013/903904
Research Article

Generalized and Stability Rational Functions for Dynamic Systems of Reactor Kinetics

1Department of Mathematics, Faculty of Science and Arts, Qassim University, P.O. Box 1300 Buraidah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

Received 27 February 2013; Revised 2 June 2013; Accepted 7 June 2013

Academic Editor: Arkady Serikov

Copyright © 2013 Ahmed E. Aboanber. 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

The base of reactor kinetics dynamic systems is a set of coupled stiff ordinary differential equations known as the point reactor kinetics equations. These equations which express the time dependence of the neutron density and the decay of the delayed neutron precursors within a reactor are first order nonlinear and essentially describe the change in neutron density within the reactor due to a change in reactivity. Outstanding the particular structure of the point kinetic matrix, a semianalytical inversion is performed and generalized for each elementary step resulting eventually in substantial time saving. Also, the factorization techniques based on using temporarily the complex plane with the analytical inversion is applied. The theory is of general validity and involves no approximations. In addition, the stability of rational function approximations is discussed and applied to the solution of the point kinetics equations of nuclear reactor with different types of reactivity. From the results of various benchmark tests with different types of reactivity insertions, the developed generalized Padé approximation (GPA) method shows high accuracy, high efficiency, and stable character of the solution.