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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2601.19172 |
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| _version_ | 1866918307868704768 |
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| author | Gao, Weiguo He, Zhansi Yin, Jia |
| author_facet | Gao, Weiguo He, Zhansi Yin, Jia |
| contents | In this paper, we propose a novel sixth-order compact time-splitting scheme, denoted as $ S_{6\text{c}}$, for solving the Dirac equation in the absence of external magnetic potentials. This method is easy to implement, and it provides a substantial reduction in computational complexity compared to the existing sixth-order splitting schemes. By incorporating a time-ordering technique, we also extend $S_{6\text{c}}$ to address problems with time-dependent potentials. Comprehensive comparisons with various time-splitting methods show that $S_{6\text{c}}$ exhibits significant advantages in terms of both precision and efficiency. Moreover, numerical results indicate that $S_{6\text{c}}$ maintains the super-resolution property for the Dirac equation in the nonrelativistic regime in the absence of external magnetic potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A sixth-order compact time-splitting Fourier pseudospectral method Gao, Weiguo He, Zhansi Yin, Jia Numerical Analysis 35Q41, 65M70, 65N35 In this paper, we propose a novel sixth-order compact time-splitting scheme, denoted as $ S_{6\text{c}}$, for solving the Dirac equation in the absence of external magnetic potentials. This method is easy to implement, and it provides a substantial reduction in computational complexity compared to the existing sixth-order splitting schemes. By incorporating a time-ordering technique, we also extend $S_{6\text{c}}$ to address problems with time-dependent potentials. Comprehensive comparisons with various time-splitting methods show that $S_{6\text{c}}$ exhibits significant advantages in terms of both precision and efficiency. Moreover, numerical results indicate that $S_{6\text{c}}$ maintains the super-resolution property for the Dirac equation in the nonrelativistic regime in the absence of external magnetic potentials. |
| title | A sixth-order compact time-splitting Fourier pseudospectral method |
| topic | Numerical Analysis 35Q41, 65M70, 65N35 |
| url | https://arxiv.org/abs/2601.19172 |