A new approach to integrals of discretizations by polarization
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913245029203968 |
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| author | Suris, Yuri B. |
| author_facet | Suris, Yuri B. |
| contents | Recently, a family of unconventional integrators for ODEs with polynomial vector fields was proposed, based on the polarization of vector fields. The simplest instance is the by now famous Kahan discretization for quadratic vector fields. All these integrators seem to possess remarkable conservation properties. In particular, it has been proved that, when the underlying ODE is Hamiltonian, its polarization discretization possesses an integral of motion and an invariant volume form. In this note, we propose a new algebraic approach to derivation of the integrals of motion for polarization discretizations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_00581 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new approach to integrals of discretizations by polarization Suris, Yuri B. Exactly Solvable and Integrable Systems Numerical Analysis Mathematical Physics Dynamical Systems Recently, a family of unconventional integrators for ODEs with polynomial vector fields was proposed, based on the polarization of vector fields. The simplest instance is the by now famous Kahan discretization for quadratic vector fields. All these integrators seem to possess remarkable conservation properties. In particular, it has been proved that, when the underlying ODE is Hamiltonian, its polarization discretization possesses an integral of motion and an invariant volume form. In this note, we propose a new algebraic approach to derivation of the integrals of motion for polarization discretizations. |
| title | A new approach to integrals of discretizations by polarization |
| topic | Exactly Solvable and Integrable Systems Numerical Analysis Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2307.00581 |