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arXiv · 1908.09143

A Pseudospectral Method for the One-Dimensional Fractional Laplacian on $\mathbb R$

Jorge Cayama·Carlota M. Cuesta·Francisco de la Hoz
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Abstract

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 $\mathbb R$, we map the unbounded domain into a finite one, then we represent the function as a trigonometrical 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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Jorge Cayama, Carlota M. Cuesta, Francisco de la Hoz. 2019-08-24. A Pseudospectral Method for the One-Dimensional Fractional Laplacian on $\mathbb R$. https://arxiv.org/abs/1908.09143

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