Numerical analysis of the homogeneous Landau equation: approximation, error estimates and simulation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911149328433152 |
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| author | Filbet, Francis Gui, Yanzhi He, Ling-Bing |
| author_facet | Filbet, Francis Gui, Yanzhi He, Ling-Bing |
| contents | We construct a numerical solution to the spatially homogeneous Landau equation with Coulomb potential on a domain $D_L$ with N retained Fourier modes. By deriving an explicit error estimate in terms of $L$ and $N$, we demonstrate that for any prescribed error tolerance and fixed time interval $[0, T ]$, there exist choices of $D_L$ and $N$ satisfying explicit conditions such that the error between the numerical and exact solutions is below the tolerance. Specifically, the estimate shows that sufficiently large $L$ and $N$ (depending on initial data parameters and $T$) can reduce the error to any desired level. Numerical simulations based on this construction are also presented. The results in particular demonstrate the mathematical validity of the spectral method proposed in the referenced literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical analysis of the homogeneous Landau equation: approximation, error estimates and simulation Filbet, Francis Gui, Yanzhi He, Ling-Bing Analysis of PDEs Numerical Analysis We construct a numerical solution to the spatially homogeneous Landau equation with Coulomb potential on a domain $D_L$ with N retained Fourier modes. By deriving an explicit error estimate in terms of $L$ and $N$, we demonstrate that for any prescribed error tolerance and fixed time interval $[0, T ]$, there exist choices of $D_L$ and $N$ satisfying explicit conditions such that the error between the numerical and exact solutions is below the tolerance. Specifically, the estimate shows that sufficiently large $L$ and $N$ (depending on initial data parameters and $T$) can reduce the error to any desired level. Numerical simulations based on this construction are also presented. The results in particular demonstrate the mathematical validity of the spectral method proposed in the referenced literature. |
| title | Numerical analysis of the homogeneous Landau equation: approximation, error estimates and simulation |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2509.09276 |