Fixed-point approximation for self-consistent transfer operators with Newton's method
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911666971607040 |
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| author | Bahsoun, Wael Froyland, Gary Phalempin, Maxence |
| author_facet | Bahsoun, Wael Froyland, Gary Phalempin, Maxence |
| contents | Self consistent transfer operators arise naturally in the study of mean-field coupled dynamical systems and are closely related to kinetic PDEs such as the Vlasov equation. Despite substantial progress on existence and uniqueness of fixed points for self-consistent transfer operators, the development of fast, reliable, and provably accurate numerical methods remains largely unresolved. In this work, we construct a nonlinear Fourier-Fejér discretisation and establish convergence of the resulting finite-dimensional fixed point to that of the original self-consistent transfer operator. Further, using the nonlinear Fourier-Fejér discretisation, we prove exponential convergence of a sequential iteration scheme and develop a Newton framework with quadratic convergence. We present numerical examples demonstrating the efficiency and flexibility of the above methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08803 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fixed-point approximation for self-consistent transfer operators with Newton's method Bahsoun, Wael Froyland, Gary Phalempin, Maxence Dynamical Systems Self consistent transfer operators arise naturally in the study of mean-field coupled dynamical systems and are closely related to kinetic PDEs such as the Vlasov equation. Despite substantial progress on existence and uniqueness of fixed points for self-consistent transfer operators, the development of fast, reliable, and provably accurate numerical methods remains largely unresolved. In this work, we construct a nonlinear Fourier-Fejér discretisation and establish convergence of the resulting finite-dimensional fixed point to that of the original self-consistent transfer operator. Further, using the nonlinear Fourier-Fejér discretisation, we prove exponential convergence of a sequential iteration scheme and develop a Newton framework with quadratic convergence. We present numerical examples demonstrating the efficiency and flexibility of the above methods. |
| title | Fixed-point approximation for self-consistent transfer operators with Newton's method |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.08803 |