A simple and fast finite difference method for the integral fractional Laplacian of variable order
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916288677281792 |
|---|---|
| author | Hao, Zhaopeng Shi, Siyuan Zhang, Zhongqiang Du, Rui |
| author_facet | Hao, Zhaopeng Shi, Siyuan Zhang, Zhongqiang Du, Rui |
| contents | For the fractional Laplacian of variable order, an efficient and accurate numerical evaluation in multi-dimension is a challenge for the nature of a singular integral. We propose a simple and easy-to-implement finite difference scheme for the multi-dimensional variable-order fractional Laplacian defined by a hypersingular integral. We prove that the scheme is of second-order convergence and apply the developed finite difference scheme to solve various equations with the variable-order fractional Laplacian. We present a fast solver with quasi-linear complexity of the scheme for computing variable-order fractional Laplacian and corresponding PDEs. Several numerical examples demonstrate the accuracy and efficiency of our algorithm and verify our theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A simple and fast finite difference method for the integral fractional Laplacian of variable order Hao, Zhaopeng Shi, Siyuan Zhang, Zhongqiang Du, Rui Numerical Analysis 65N06, 65N12, 65T50, 35R11, 26A33 For the fractional Laplacian of variable order, an efficient and accurate numerical evaluation in multi-dimension is a challenge for the nature of a singular integral. We propose a simple and easy-to-implement finite difference scheme for the multi-dimensional variable-order fractional Laplacian defined by a hypersingular integral. We prove that the scheme is of second-order convergence and apply the developed finite difference scheme to solve various equations with the variable-order fractional Laplacian. We present a fast solver with quasi-linear complexity of the scheme for computing variable-order fractional Laplacian and corresponding PDEs. Several numerical examples demonstrate the accuracy and efficiency of our algorithm and verify our theory. |
| title | A simple and fast finite difference method for the integral fractional Laplacian of variable order |
| topic | Numerical Analysis 65N06, 65N12, 65T50, 35R11, 26A33 |
| url | https://arxiv.org/abs/2406.10524 |