Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation
A high-order accuracy numerical method is proposed to solve the (1+1)-dimensional nonlinear Dirac equation in this work. We construct the compact finite difference scheme for the spatial discretization and obtain a nonlinear ordinary differential system. For the temporal discretization, the implicit...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/3634815 |
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| _version_ | 1832564950591078400 |
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| author | Jing-Jing Zhang Xiang-Gui Li Jing-Fang Shao |
| author_facet | Jing-Jing Zhang Xiang-Gui Li Jing-Fang Shao |
| author_sort | Jing-Jing Zhang |
| collection | DOAJ |
| description | A high-order accuracy numerical method is proposed to solve the (1+1)-dimensional nonlinear Dirac equation in this work. We construct the compact finite difference scheme for the spatial discretization and obtain a nonlinear ordinary differential system. For the temporal discretization, the implicit integration factor method is applied to deal with the nonlinear system. We therefore develop two implicit integration factor numerical schemes with full discretization, one of which can achieve fourth-order accuracy in both space and time. Numerical results are given to validate the accuracy of these schemes and to study the interaction dynamics of the nonlinear Dirac solitary waves. |
| format | Article |
| id | doaj-art-45d8b9f766404e98bf02da86d857b91d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-45d8b9f766404e98bf02da86d857b91d2025-02-03T01:09:45ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/36348153634815Compact Implicit Integration Factor Method for the Nonlinear Dirac EquationJing-Jing Zhang0Xiang-Gui Li1Jing-Fang Shao2School of Applied Sciences, Beijing Information Science and Technology University, Beijing 100192, ChinaSchool of Applied Sciences, Beijing Information Science and Technology University, Beijing 100192, ChinaSchool of Applied Sciences, Beijing Information Science and Technology University, Beijing 100192, ChinaA high-order accuracy numerical method is proposed to solve the (1+1)-dimensional nonlinear Dirac equation in this work. We construct the compact finite difference scheme for the spatial discretization and obtain a nonlinear ordinary differential system. For the temporal discretization, the implicit integration factor method is applied to deal with the nonlinear system. We therefore develop two implicit integration factor numerical schemes with full discretization, one of which can achieve fourth-order accuracy in both space and time. Numerical results are given to validate the accuracy of these schemes and to study the interaction dynamics of the nonlinear Dirac solitary waves.http://dx.doi.org/10.1155/2017/3634815 |
| spellingShingle | Jing-Jing Zhang Xiang-Gui Li Jing-Fang Shao Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation Discrete Dynamics in Nature and Society |
| title | Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation |
| title_full | Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation |
| title_fullStr | Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation |
| title_full_unstemmed | Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation |
| title_short | Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation |
| title_sort | compact implicit integration factor method for the nonlinear dirac equation |
| url | http://dx.doi.org/10.1155/2017/3634815 |
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