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

Abstract

A number of 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. 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. It is robust to stiff problems and suitable for nonlinear systems. To demonstrate performance, the results of the proposed method are compared with the expanded Taylor series method and the procedure is tested using various sampling times and input signals.