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The present study develops a new method for calculating reactivity by using the Gauss-Legendre quadrature to numerically solve the inverse point kinetic equation. This quadrature can use different nodes and weights from Legendre polynomials with different orders. The results show good accuracy for polynomial higher orders with small time steps. The discretization obtained with the Gauss-Legendre quadrature allows expressing the reactivity calculation in the form of linear convolutions for integral dependence. The differential is approximated with a special quadrature by taking advantage of the behavior of the Lagrange polynomials. Results can be improved, but increases computational cost. It is concluded that the method developed here can be implemented in a reactivity digital meter that measures neutron populations as input signals for a nuclear reactor. [ABSTRACT FROM AUTHOR]

In the present study, the implicit order 1.5 Runge-Kutta scheme is proposed to numerically solve stochastic point kinetic equations by considering different reactivity values. A covariance matrix is obtained by applying the one-velocity diffusion theory for a nuclear reactor. It is assumed that at initial time a neutron pulse is injected into a non-multiplicative assembly. The results obtained by applying this method are accurate, based on the standard deviation and the expected value, when compared to other methods reported in the literature. It is concluded that the proposed method is accurate for calculating neutron density and delayed neutron precursor concentration. [ABSTRACT FROM AUTHOR]