The numerical solution of the point kinetics equation using matrix exponential method

Abstract

Many numerical methods are used to solve the point kinetics equations in nuclear dynamics. However the point kinetics equation is characterized by stiff nonlinear ordinary differential equations, which is a severe problem in numerical solution and results in the need for small time steps in a computational scheme. So it is difficult to obtain accurate results. In this work we propose a numerical solution to the point kinetics equations. The proposed method is based on the matrix exponential method under the zero order hold (ZOH) assumption and includes the automatic correction of rounding errors. In order to evaluate the performance, the presented method is compared with Taylor-Lie series with variable inputs.