Stochastic Neutron Population with Temperature Feedback Effects Using the Implicit Runge-Kutta Scheme

Numerical simulations are carried out to study the temporal behaviour of the neutron population and the concentration of delayed neutron precursors in a nuclear power plant by solving the stochastic equations of point kinetics considering temperature feedback effects. These equations are solved through the implicit Runge-Kutta scheme of order 1.5 with up to 500 Brownian motions. The computational cost can be reduced by using the analytical expression of the square root of the covariance matrix. The numerical simulations present good approximations in terms of means and standard deviations in agreement with other results using different numerical methods. The proposed scheme has good accuracy, it can be considered as an alternative method to simulate the time evolution of the stochastic density of the neutron population and the concentration of delayed neutron precursors considering temperature feedback effects.