A pseudospectral method for the one-dimensional fractional Laplacian on R

被引：7

作者：

Cayama, Jorge ^{[1
]}

Cuesta, Carlota M. ^{[2
]}

de la Hoz, Francisco ^{[3
]}

机构：

[1] BCAM Basque Ctr Appl Math, Alameda Mazarredo 14, Bilbao 48009, Spain

[2] Univ Basque Country UPV, Fac Sci & Technol, Dept Math, EHU, Barrio Sarriena S-N, Leioa 48940, Spain

[3] Univ Basque Country UPV, Fac Sci & Technol, Dept Appl Math & Stat & Operat Res, EHU, Barrio Sarriena S-N, Leioa 48940, Spain

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2021年 / 389卷 / 389期

关键词：

Fractional Laplacian; Pseudospectral methods; Rational Chebyshev functions; Nonlocal Fisher's equation; Accelerating fronts; EXTERNAL FORCE-FIELDS; DIFFERENTIAL-EQUATIONS; ANOMALOUS DIFFUSION; FRONT PROPAGATION; SPECTRAL METHODS; TRAVELING-WAVES; FISHER EQUATION; LEVY FLIGHTS; MODELS; MEDIA;

D O I：

10.1016/j.amc.2020.125577

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 methods fractional Laplacian in the monostable case. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：21

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