Error estimates of time-splitting schemes for nonlinear Klein--Gordon equation with rough data
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917935086305280 |
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| author | Ji, Lun Zhao, Xiaofei |
| author_facet | Ji, Lun Zhao, Xiaofei |
| contents | In this work, we consider the convergence analysis of time-splitting schemes for the nonlinear Klein--Gordon/wave equation under rough initial data. The optimal error bounds of the Lie splitting and the Strang splitting are established with sharp dependence on the regularity index of the solution from a wide range that is approaching the lower bound for well-posedness. Particularly for very rough data, the technique of discrete Bourgain space is utilized and developed, which can apply for general second-order wave models. Numerical verifications are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error estimates of time-splitting schemes for nonlinear Klein--Gordon equation with rough data Ji, Lun Zhao, Xiaofei Numerical Analysis 65M12, 65M15, 65M70, 81Q05, 35Q40 In this work, we consider the convergence analysis of time-splitting schemes for the nonlinear Klein--Gordon/wave equation under rough initial data. The optimal error bounds of the Lie splitting and the Strang splitting are established with sharp dependence on the regularity index of the solution from a wide range that is approaching the lower bound for well-posedness. Particularly for very rough data, the technique of discrete Bourgain space is utilized and developed, which can apply for general second-order wave models. Numerical verifications are provided. |
| title | Error estimates of time-splitting schemes for nonlinear Klein--Gordon equation with rough data |
| topic | Numerical Analysis 65M12, 65M15, 65M70, 81Q05, 35Q40 |
| url | https://arxiv.org/abs/2502.16876 |