Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Padé approximations via the analytical inversion method

TLDR: In this paper, a method based on Pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity, which is applicable equally well to nonlinear problems, where the reactivity depends on the neutron density through temperature feedback.

Abstract: A method based on the Pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity. The technique consists of treating explicitly the roots of the inhour formula. A significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation, which usually would make the Pade approximation inaccurate. Also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the Pade approximations. Results are presented for several cases of Pade approximations using various options of the method with different types of reactivity. The formalism is applicable equally well to non-linear problems, where the reactivity depends on the neutron density through temperature feedback. It was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases.