A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems
Author
Source
Science and Technology of Nuclear Installations
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-10-01
Country of Publication
Egypt
No. of Pages
15
Abstract EN
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.
American Psychological Association (APA)
Hamada, Yasser Mohamed. 2018. A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems. Science and Technology of Nuclear Installations،Vol. 2018, no. 2018, pp.1-15.
https://search.emarefa.net/detail/BIM-1214989
Modern Language Association (MLA)
Hamada, Yasser Mohamed. A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems. Science and Technology of Nuclear Installations No. 2018 (2018), pp.1-15.
https://search.emarefa.net/detail/BIM-1214989
American Medical Association (AMA)
Hamada, Yasser Mohamed. A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems. Science and Technology of Nuclear Installations. 2018. Vol. 2018, no. 2018, pp.1-15.
https://search.emarefa.net/detail/BIM-1214989
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1214989