Symmetric-conjugate splitting methods for evolution equations of parabolic type
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913189409587200 |
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| author | Blanes, Sergio Casas, Fernando González, Cesáreo Thalhammer, Mechthild |
| author_facet | Blanes, Sergio Casas, Fernando González, Cesáreo Thalhammer, Mechthild |
| contents | The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant applications include nonreversible systems and ground state computations for linear Schrödinger equations based on the imaginary time propagation. Numerical examples confirm the favourable error behaviour of higher-order symmetric-conjugate splitting methods and illustrate the usefulness of a time stepsize control, where the local error estimation relies on the computation of the imaginary parts and thus requires negligible costs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric-conjugate splitting methods for evolution equations of parabolic type Blanes, Sergio Casas, Fernando González, Cesáreo Thalhammer, Mechthild Numerical Analysis Computational Physics 65J10, 65L04, 65M12 The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant applications include nonreversible systems and ground state computations for linear Schrödinger equations based on the imaginary time propagation. Numerical examples confirm the favourable error behaviour of higher-order symmetric-conjugate splitting methods and illustrate the usefulness of a time stepsize control, where the local error estimation relies on the computation of the imaginary parts and thus requires negligible costs. |
| title | Symmetric-conjugate splitting methods for evolution equations of parabolic type |
| topic | Numerical Analysis Computational Physics 65J10, 65L04, 65M12 |
| url | https://arxiv.org/abs/2401.04196 |