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Tumelero F, Petersen CZ, Gonçalves GA, Schramm M. Polynomial approach method to solve the neutron point kinetics equations with use of the analytic continuation. KERNTECHNIK 2016. [DOI: 10.3139/124.110600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
AbstractIn this work, we report a solution to solve the Neutron Point Kinetics Equations applying the Polynomial Approach Method. The main idea is to expand the neutron density and delayed neutron precursors as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions and the analytical continuation is used to determine the solutions of the next intervals. A genuine error control is developed based on an analogy with the Rest Theorem. For illustration, we also report simulations for different approaches types (linear, quadratic and cubic). The results obtained by numerical simulations for linear approximation are compared with results in the literature.
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Affiliation(s)
- F. Tumelero
- 1Universidade Federal de Pelotas, Programa de Pós Graduação em Modelagem Matemática, Campus Universitário Capão do Leão s/n, 96010-610 Capão do Leão, RS, Brazil, E-mail:
| | - C. Z. Petersen
- 2Universidade Federal de Pelotas, Programa de Pós Graduação em Modelagem Matemática, Campus Universitário Capão do Leão s/n, 96010-610 Capão do Leão, RS, Brazil, E-mail corresponding author:
| | - G. A. Gonçalves
- 3Universidade Federal de Pelotas, Programa de Pós Graduação em Modelagem Matemática, Campus Universitário Capão do Leão s/n, 96010-610 Capão do Leão, RS, Brazil, E-mail:
| | - M. Schramm
- 4Universidade Federal do Rio Grande do Sul, Programa de Pós-graduação em Engenharia Mecânica, Rua Sarmento Leite, 425, 90050-170 Porto Alegre, RS, Brazil, E-mail:
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Wollmann da Silva M, Bogado Leite S, Vilhena M, Bodmann B. On an analytical representation for the solution of the neutron point kinetics equation free of stiffness. ANN NUCL ENERGY 2014. [DOI: 10.1016/j.anucene.2014.03.032] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Stiffness treatment of differential equations for the point reactor dynamic systems. PROGRESS IN NUCLEAR ENERGY 2014. [DOI: 10.1016/j.pnucene.2013.12.004] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Li H, Chen W, Luo L, Zhu Q. A new integral method for solving the point reactor neutron kinetics equations. ANN NUCL ENERGY 2009. [DOI: 10.1016/j.anucene.2008.11.033] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Lee C, Rottler S. Analytic solutions of the multigroup space-time reactor kinetics equations—I. ANN NUCL ENERGY 1986. [DOI: 10.1016/0306-4549(86)90053-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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