A pseudospectral method for the one-dimensional fractional Laplacian on R
In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map the unbounded domain into a finite one, and represent the resulting function as...
| Authors: | , , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Basque Center for Applied Mathematics (BCAM) |
| Repository: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1453 |
| Online Access: | http://hdl.handle.net/20.500.11824/1453 |
| Access Level: | Open access |
| Keyword: | Accelerating fronts Fractional Laplacian Nonlocal Fisher's equation Pseudospectral methods Rational Chebyshev functions |
| Summary: | In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map the unbounded domain into a finite one, and represent the resulting function as a trigonometric series. Therefore, the central point of this paper is the computation of the fractional Laplacian of an elementary trigonometric function. As an application of the method, we also do the simulation of Fisher's equation with fractional Laplacian in the monostable case. |
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