Approximate solution of the point reactor kinetic equations of average one-group of delayed neutrons for step reactivity insertion

The understanding of the time-dependent behaviour of the neutron population in a nuclear reactor in response to either a planned or unplanned change in the reactor conditions is of great importance to the safe and reliable operation of the reactor. In this study two analytical methods have been presented to solve the point kinetic equations of average one-group of delayed neutrons. These methods which are both approximate solution of the point reactor kinetic equations are compared with a numerical solution using the Euler's first order method. To obtain accurate solution for the Euler method, a relatively small time step was chosen for the numerical solution. These methods are applied to different types of reactivity to check the validity of the analytical method by comparing the analytical results with the numerical results. From the results, it is observed that the analytical solution agrees well with the numerical solution.