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Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems |
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| Authors: | Zhaoxia Chen Xiong You Wei Shi Zhongli Liu |
| Affiliation: | 1. Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, PR China;2. State Key Laboratory for Novel Software Technology at Nanjing University, Nanjing University, Nanjing 210093, PR China;1. School of Science, Shandong Jiaotong University, Jinan 250357, China;2. Department of Mathematics, Zhejiang University, Hangzhou 310028, China;3. School of Science, Zhejiang Normal University, Hangzhou 310036, China;1. Department of Chemistry, University of Perugia, via Elce di Sotto, 8 06123 Perugia, Italy;2. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1 06123 Perugia, Italy |
| Abstract: | The ERKN methods proposed by H. Yang et al. Comput. Phys. Comm. 180 (2009) 1777] are an important improvement of J.M. Franco?s ARKN methods for perturbed oscillators J.M. Franco, Comput. Phys. Comm. 147 (2002) 770]. This paper focuses on the symmetry and symplecticity conditions for ERKN methods solving oscillatory Hamiltonian systems. Two examples of symmetric and symplectic ERKN (SSERKN) methods of orders two and four respectively are constructed. The phase and stability properties of the new methods are analyzed. The results of numerical experiments show the robustness and competence of the SSERKN methods compared with some well-known methods in the literature. |
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