Generalization of the analytical exponential model for homogeneous reactor kinetics equations (Q442851)

Summary: A mathematical form for two energy groups of the three-dimensional homogeneous reactor kinetics equations and the 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 the two energy groups of the point kinetics equations in matrix form. A generalization of the analytical exponential model (GAEM) is developed for solving the 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 \texttt{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.