Numerical Techniques for the Neutron Diusion Equations in the Nuclear Reactors

Abstract

The space-time neutron diffusion equations with multi-group of delayed neutrons are a couple of the stiff nonlinear partial differential equations. The finite difference method is used to reduce the partial differential equations into ordinary differential equations. This ordinary differential equations are rewritten in a matrix form. The general solution of the matrix differential equation contains the exponential function of the coefficient matrix. The numerical techniques for processing the exponential function of the coefficient matrix are presented using analytical method and fundamental matrix method. The eigenvalues of the coefficient matrix are calculated numerically using FORTRAN computer code based on Laguerre’s method. The fundamental matrix and its inverse are calculated analytically for two energy groups of reactor kinetics and one group of precursor delayed neutrons. The numerical techniques are applied to three-dimensional space-time neutron diffusion equations with average one group of delayed neutrons in the different nuclear reactors. The results of numerical technique codes are compared with the results of traditional codes. ∗Corresponding author: Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt. 650 A. Nahla, F. Al-Malki and M. Rokaya