Higher-Order Finite Difference Methods for the Tempered Fractional Laplacian
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915760687808512 |
|---|---|
| author | Wang, Mingyi Wang, Dongling |
| author_facet | Wang, Mingyi Wang, Dongling |
| contents | This paper presents a general framework of high-order finite difference (HFD) schemes for the tempered fractional Laplacian (TFL) based on new generating functions obtained from the discrete symbols. Specifically, for sufficiently smooth functions, the resulting discretizations achieve high-order convergence with orders $p=4, 6, 8$. The discrete operators lead to Toeplitz stiffness matrices, allowing efficient matrix-vector multiplications via fast algorithms. Building on these approximations, HFD methods are formulated for solving TFL equations, and their stability and convergence are rigorously analyzed. Numerical simulations confirm the effectiveness of the proposed methods, showing excellent agreement with the theoretical predictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21388 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher-Order Finite Difference Methods for the Tempered Fractional Laplacian Wang, Mingyi Wang, Dongling Numerical Analysis This paper presents a general framework of high-order finite difference (HFD) schemes for the tempered fractional Laplacian (TFL) based on new generating functions obtained from the discrete symbols. Specifically, for sufficiently smooth functions, the resulting discretizations achieve high-order convergence with orders $p=4, 6, 8$. The discrete operators lead to Toeplitz stiffness matrices, allowing efficient matrix-vector multiplications via fast algorithms. Building on these approximations, HFD methods are formulated for solving TFL equations, and their stability and convergence are rigorously analyzed. Numerical simulations confirm the effectiveness of the proposed methods, showing excellent agreement with the theoretical predictions. |
| title | Higher-Order Finite Difference Methods for the Tempered Fractional Laplacian |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.21388 |