Keywords: nonlinear equations, neutron point kinetics equations, temperature feedback reactivity, ramp reactivity, multi–group delayed neutrons, nuclear reactors, reactor dynamics, nuclear energy, nuclear power, finite difference method
Solution of non–linear neutron point kinetics equations with feedback reactivity in nuclear reactor dynamics
In this paper, an efficient numerical procedure for calculating the solution of the non–linear neutron point kinetics equations in the field of nuclear reactor dynamics is presented. The explicit finite difference method is applied to solve the non–linear neutron point kinetics equations with temperature feedback reactivity. The numerical solution obtained by explicit finite difference scheme is an approximate solution based on neutron density, the precursor's concentration of multi–group delayed neutrons, and the reactivity function. The method is investigated over data of nuclear reactor–type compositions, with appropriate initial conditions applying in three types of reactivity: step, ramp and temperature feedback. The computational results show that this numerical approximation method is straightforward and effective for solving the non–linear point kinetics equations. Numerical results addressing the time behaviour of neutron density and results of this method with different types of reactivity are presented graphically. The comparisons of results with other referred methods are also discussed.