Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle
| Autor: | Zhu-Yan Shao, Xing-Qiu Zhang, Jian-Qiang Gao, Yi Wei, Xiao-Feng Yang |
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| Rok vydání: | 2019 |
| Předmět: |
Conservation law
Multidisciplinary Mathematics and computing Physics Semi-implicit Euler method lcsh:R Structure (category theory) lcsh:Medicine 01 natural sciences Article 010305 fluids & plasmas 010101 applied mathematics symbols.namesake Fourier transform Variational principle 0103 physical sciences symbols Applied mathematics lcsh:Q Symplectic integrator 0101 mathematics lcsh:Science Korteweg–de Vries equation Mathematics Numerical stability |
| Zdroj: | Scientific Reports, Vol 9, Iss 1, Pp 1-10 (2019) Scientific Reports |
| ISSN: | 2045-2322 |
| DOI: | 10.1038/s41598-019-52419-8 |
| Popis: | The variational principle is used to construct a multi-symplectic structure of the generalized KdV-type equation. Accordingly, the local energy conservation law, the local momentum conservation law, and the Cartan form of the generalized KdV-type equation are given. An explicit multi-symplectic scheme for the generalized KdV equation based on the Fourier pseudo-spectral method and the symplectic Euler scheme is constructed. Through a numerical examination, the explicit multi-symplectic Fourier pseudo-spectral scheme for the generalized KdV equation not only preserve the discrete global energy conservation law and the global momentum conservation law with high accuracy, but show long-time numerical stability as well. |
| Databáze: | OpenAIRE |
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