A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems
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 se...
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| Format: | Article |
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Wiley
2018-01-01
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| Series: | Science and Technology of Nuclear Installations |
| Online Access: | http://dx.doi.org/10.1155/2018/7105245 |
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| author | Yasser Mohamed Hamada |
| author_facet | Yasser Mohamed Hamada |
| author_sort | Yasser Mohamed Hamada |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a39616f392824d9aa25067791f6e4cf8 |
| institution | Kabale University |
| issn | 1687-6075 1687-6083 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Science and Technology of Nuclear Installations |
| spelling | doaj-art-a39616f392824d9aa25067791f6e4cf82025-02-03T05:44:40ZengWileyScience and Technology of Nuclear Installations1687-60751687-60832018-01-01201810.1155/2018/71052457105245A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical SystemsYasser Mohamed Hamada0Department of Basic Science, Faculty of Computers & Informatics, Suez Canal University, Ismailia 41522, EgyptA 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.http://dx.doi.org/10.1155/2018/7105245 |
| spellingShingle | Yasser Mohamed Hamada A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems Science and Technology of Nuclear Installations |
| title | A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems |
| title_full | A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems |
| title_fullStr | A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems |
| title_full_unstemmed | A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems |
| title_short | A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems |
| title_sort | new accurate numerical method based on shifted chebyshev series for nuclear reactor dynamical systems |
| url | http://dx.doi.org/10.1155/2018/7105245 |
| work_keys_str_mv | AT yassermohamedhamada anewaccuratenumericalmethodbasedonshiftedchebyshevseriesfornuclearreactordynamicalsystems AT yassermohamedhamada newaccuratenumericalmethodbasedonshiftedchebyshevseriesfornuclearreactordynamicalsystems |