Numerical Approximation for Fractional Neutron Transport Equation
Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6676640 |
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| _version_ | 1832547053014614016 |
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| author | Zhengang Zhao Yunying Zheng |
| author_facet | Zhengang Zhao Yunying Zheng |
| author_sort | Zhengang Zhao |
| collection | DOAJ |
| description | Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition. |
| format | Article |
| id | doaj-art-f41bbb69133f43048d028935c35d2842 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f41bbb69133f43048d028935c35d28422025-02-03T06:46:15ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66766406676640Numerical Approximation for Fractional Neutron Transport EquationZhengang Zhao0Yunying Zheng1Department of Fundamental Courses, Shanghai Customs College, Shanghai 201204, ChinaSchool of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, ChinaFractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition.http://dx.doi.org/10.1155/2021/6676640 |
| spellingShingle | Zhengang Zhao Yunying Zheng Numerical Approximation for Fractional Neutron Transport Equation Journal of Mathematics |
| title | Numerical Approximation for Fractional Neutron Transport Equation |
| title_full | Numerical Approximation for Fractional Neutron Transport Equation |
| title_fullStr | Numerical Approximation for Fractional Neutron Transport Equation |
| title_full_unstemmed | Numerical Approximation for Fractional Neutron Transport Equation |
| title_short | Numerical Approximation for Fractional Neutron Transport Equation |
| title_sort | numerical approximation for fractional neutron transport equation |
| url | http://dx.doi.org/10.1155/2021/6676640 |
| work_keys_str_mv | AT zhengangzhao numericalapproximationforfractionalneutrontransportequation AT yunyingzheng numericalapproximationforfractionalneutrontransportequation |