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This study presents a method that applies the Gauss-Legendre quadrature to approximate the integral contained in the inverse equation of point kinetics for the calculation of nuclear reactivity. Fluctuations in a neutron population of a nuclear reactor are assumed to be multiplicative Gaussian white noise around the mean. A modified low-pass filter performs fluctuation reductions by considering a symmetrical sampling window for both low and high frequencies. Filter parameters such as the filter constant and the sampling window are optimized for different values of standard deviation. An error surface is estimated from differences between the analytical values and the numerical values of reactivity, which is minimized to determine optimal parameters. It is concluded that the method presented here can be considered as an alternative method to reduce fluctuations in the calculation of nuclear reactivity and can be implemented in a digital reactivity meter.

This article presents a study based on a series of numerical experiments. It demonstrates the possibility of reducing fluctuations in the calculation of reactivity using the second Bernoulli number based on the approximation of the Euler-Maclaurin formula. This approach requires knowledge of the first three derivatives, which are implemented progressively. The fluctuations are assumed to occur around an average value of the neutron density with a Gaussian distribution. Jitter reduction is performed with a first-order delayed low-pass filter for different forms of neutron population density, with different time steps and with different filter constants. The numerical results show that the method can be used as a digital reactivity meter.

In this study, the primary aim is to examine the reductions in fluctuations in nuclear reactivity calculations by discretizing neutron density history in an inverse point kinetics equation. The Euler-Maclaurin formula is applied with neutron density's infinite even and odd derivatives and the impulse response function. The convergence approximation is calculated by means of the Laurent series, which contains the convergence of infinite Bernoulli numbers. The numerical simulations performed show that it is possible to reduce fluctuations in reactivity by considering a Gaussian noise around a mean value of the neutron density when the low-pass filter is used with different values of the filtering time constant and different values of the standard deviation. It is concluded that for neutron density of the exponential and cubic shape the reductions in reactivity calculation obtained can nearly reach 80%.

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