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Research Article

A Precision Benchmark Suite for Nuclear Reactor Point Kinetics Equations via Converged Accelerated Taylor Series (CATS)

Pages 1497-1533 | Received 14 Jun 2023, Accepted 28 Aug 2023, Published online: 21 Feb 2024

References

  • B. QUINTERO-LEYVA, “CORE: A Numerical Algorithm to Solve the Point Kinetics Equations,” Ann. Nucl. Energy, 35, 2136 (2008); http://dx.doi.org/10.1016/j.anucene.2008.07.002.
  • J. SANCHEZ, “On the Numerical Solution of Point Reactor Kinetics Equations by the Generalized Runge-Kutta Methods,” Nucl. Sci. Eng., 103, 94 (1989); http://dx.doi.org/10.13182/NSE89-A23663.
  • X. YANG and T. JEVREMOVIC, “Revisiting the Rosenbrock Numerical Solutions of the Reactor Point Kinetics Equation with Numerous Examples,” Nucl. Technol. Radiat. Prot., 24, 1, 3 (2009); http://dx.doi.org/10.2298/NTRP0901003Y.
  • H. LI et al., “A New Integral Method for Solving the Point Reactor Neutron Kinetics Equations,” Ann. Nucl. Energy, 36, 427 (2009); http://dx.doi.org/10.1016/j.anucene.2008.11.033.
  • Y. CHAO and A. ATTARD, “A Resolution of the Stiffness Problem of Reactor Kinetics,” Nucl. Sci. Eng., 90, 40 (1985); http://dx.doi.org/10.13182/NSE85-A17429.
  • A. E. ABOANBER and A. A. NAHLA, “On Padé Approximations to the Exponential Function and Application to Point Kinetics Equations,” Prog. Nucl. Energy, 44, 347 (2004); http://dx.doi.org/10.1016/j.pnucene.2004.07.003.
  • J. A. W. DA NOBREGA, “A New Solution of the Point Kinetics Equations,” Nucl. Sci. Eng., 46, 366 (1971); http://dx.doi.org/10.13182/NSE71-A22373.
  • C. Z. PETERSEN et al., “An Analytical Solution of the Point Kinetics Equations with Time-Variable Reactivity by the Decomposition Method,” Prog. Nucl. Energy, 53, 1091 (2011); http://dx.doi.org/10.1016/j.pnucene.2011.01.001.
  • R. G. KEEPIN, Physics of Nuclear Kinetics, Addison-Wesley (1965).
  • M. KINARD and E. ALLEN, “Efficient Numerical Solution of Point Kinetics Equations in Nuclear Dynamics,” Ann. Nucl. Energy, 31, 1039 (2004); http://dx.doi.org/10.1016/j.anucene.2003.12.008.
  • P. PICCA, R. FURFARO, and B. D. GANAPOL, “A Highly Accurate Technique for the Solution of the Non-Linear Point Kinetics Equations,” Ann. Nucl. Energy, 58, 43 (2013); http://dx.doi.org/10.1016/j.anucene.2013.03.004.
  • B. D. GANAPOL, “A Refined Way of Solving Reactor Point Kinetics Equations for Imposed Reactivity Insertion,” Nucl. Technol. Radiat. Prot., 24, 157 (2009); http://dx.doi.org/10.2298/NTRP0903157G.
  • A. A. NAHLA, “An Efficient Technique for the Point Reactor Kinetic Equations with Newtonian Temperature Feedback Effects,” Ann. Nucl. Energy, 38, 2810 (2011); http://dx.doi.org/10.1016/j.anucene.2011.08.021.
  • M. IZUMI and T. NODA, “An Implicit Method for Solving the Lumped Parameter Reactor-Kinetics Equations by Repeated Extrapolation,” Nucl. Sci. Eng., 41, 299 (1971); http://dx.doi.org/10.13182/NSE70-A20718.
  • H. LI et al., “A New Integral Method for Solving the Point Reactor Neutron Kinetics Equations,” Ann. Nucl. Energy, 36, 427 (2009); http://dx.doi.org/10.1016/j.anucene.2008.11.033.
  • D. L. HETRICK, Dynamics of Nuclear Reactors, The University of Chicago Press, Chicago, Illinois (1971).
  • J. J. KAGANOVE, “Numerical Solution of the One-Group Space-Independent Reactor Kinetics Equations for Neutron Density Given Excess Reactivity,” ANL- 6132, Argonne National Laboratory (1960).
  • B. D. GANAPOL et al., “The Solution of the Point Kinetics Equations via Convergence Acceleration Taylor Series (CATS),” Proc. Topl. Mtg. Advances in Reactors Physics (PHYSOR 2012), Knoxville, Tennessee, April 15–20, 2012, American Nuclear Society (2012).
  • B. D. GANAPOL, “A Highly Accurate Algorithm for the Solution of the Point Kinetics Equations,” Ann. Nucl. Energy, 62, 564 (2013); http://dx.doi.org/10.1016/j.anucene.2012.06.007.
  • D. MCMAHON and A. PIERSON, “A Taylor Series Solution of the Reactor Point Kinetics Equations,” arXiv:1001.4100v2 (2010).
  • A. A. NAHLA, “Taylor Series Method for Solving the Nonlinear Point Kinetics Equations,” Nucl. Eng. Des., 241, 5, 1592 (2011); http://dx.doi.org/10.1016/j.nucengdes.2011.02.016.
  • J. BASKEN and J. D. LEWINS, “Power Series Solutions of the Reactor Kinetics Equations,” Nucl. Sci. Eng., 122, 407 (1996); http://dx.doi.org/10.13182/NSE96-A24175.
  • J. VIGIL, “Solution of the Reactor Kinetics Equations by Analytic Continuation,” Nucl. Sci. Eng., 29, 392 (1967); http://dx.doi.org/10.13182/NSE29-03-392.
  • A. E. ABOANBER and Y. M. HAMADA, “PWS: An Efficient Code System for Solving Space-Independent Nuclear Reactor Dynamics,” Ann. Nucl. Energy, 29, 2159 (2002); http://dx.doi.org/10.1016/S0306-4549(02)00034-8.
  • A. E. ABOANBER and Y. M. HAMADA, “Power Series Solution (PWS) of Nuclear Reactor Dynamics with Newtonian Temperature Feedback,” Ann. Nucl. Energy, 30, 1111 (2003); http://dx.doi.org/10.1016/S0306-4549(03)00033-1.
  • Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, pp. 16, 806, 886, M. ABRAMOWITZ and I. STEGUN, Eds., Dover Publications, New York (1972).
  • A. SIDI, Practical Extrapolations Methods, Cambridge University Press, Cambridge (2003).
  • D. L. HETRICK, Dynamics of Nuclear Reactors, American Nuclear Society (1993).
  • E. SCHIASSI et al., “Physics-Informed Neural Networks for the Point Kinetics Equations for Nuclear Reactor Dynamics,” Ann. Nucl. Energy, 167, 1 (2022); http://dx.doi.org/10.1016/j.anucene.2021.108833.
  • General Leibniz Rule, Wikipedia; https://en.wikipedia.org/wiki/General_Leibniz_rule (July 2023).
  • Bessel, Wolfram Research; https://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/20/ShowAll.html (2023).