Efficient stochastic model for the point kinetics equations |
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Authors: | Abdallah A Nahla Adel M Edress |
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Institution: | 1. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypta.nahla@science.tanta.edu.eg;3. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt |
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Abstract: | A new stochastic model for the point kinetics equations with I-delayed neutron precursor groups is presented. In this stochastic model, the point kinetics equations are separated into three terms: prompt neutrons, delayed neutrons and external neutrons source. The matrix form of the efficient stochastic model is solved by a semi-analytical method. The semi-analytical method is based on the exponential function of the coefficient matrix. The eigenvalues of the coefficient matrix and Gaussian elimination are used to calculate this exponential function. The mean and standard deviation of neutron and precursor populations of the efficient stochastic model with step, ramp, and sinusoidal reactivities are computed. The results of the efficient stochastic model are compared with the results of Allen's stochastic model for the point kinetics equations. This comparison confirms that the efficient stochastic model is an accurate model compared with the deterministic point kinetics equations. This stochastic model is efficient to study the natural behavior of neutron and precursor populations in the nuclear reactor dynamics. |
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Keywords: | Itô stochastic differential equation exponential function of matrix multi-group precursor concentration variance and covariance matrix 82D75 60H35 |
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