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Roul P, Rohil V, Espinosa-Paredes G, Obaidurrahman K. An efficient computational technique for solving a fractional-order model describing dynamics of neutron flux in a nuclear reactor. ANN NUCL ENERGY 2023. [DOI: 10.1016/j.anucene.2023.109733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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Hamada YM. Nonlinear fractional diffusion model for space-time neutron dynamics. PROGRESS IN NUCLEAR ENERGY 2022. [DOI: 10.1016/j.pnucene.2022.104441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Espinosa-Martínez EG, François JL, Martin-del-Campo C, Maleki Moghaddam N. Time-space fractional neutron point kinetics: Theory and simulations. ANN NUCL ENERGY 2020. [DOI: 10.1016/j.anucene.2020.107448] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Roul P, Madduri H, Obaidurrahman K. An implicit finite difference method for solving the corrected fractional neutron point kinetics equations. PROGRESS IN NUCLEAR ENERGY 2019. [DOI: 10.1016/j.pnucene.2019.02.002] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems. SCIENCE AND TECHNOLOGY OF NUCLEAR INSTALLATIONS 2018. [DOI: 10.1155/2018/7105245] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A new method based on shifted Chebyshev series of the first kind is introduced to solve stiff linear/nonlinear systems of the point kinetics equations. The total time interval is divided into equal step sizes to provide approximate solutions. The approximate solutions require determination of the series coefficients at each step. These coefficients can be determined by equating the high derivatives of the Chebyshev series with those obtained by the given system. A new recurrence relation is introduced to determine the series coefficients. A special transformation is applied on the independent variable to map the classical range of the Chebyshev series from [-1,1] to [0,h]. The method deals with the Chebyshev series as a finite difference method not as a spectral method. Stability of the method is discussed and it has proved that the method has an exponential rate of convergence. The method is applied to solve different problems of the point kinetics equations including step, ramp, and sinusoidal reactivities. Also, when the reactivity is dependent on the neutron density and step insertion with Newtonian temperature feedback reactivity and thermal hydraulics feedback are tested. Comparisons with the analytical and numerical methods confirm the validity and accuracy of the method.
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Vyawahare VA, Espinosa-Paredes G. BWR stability analysis with sub-diffusive and feedback effects. ANN NUCL ENERGY 2017. [DOI: 10.1016/j.anucene.2017.06.059] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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