Numerical Approximation of the Fractional Laplacian on \mathbb R Using Orthogonal Families

2020/01/23 by Jorge Cayama, Cayama, Jorge, Carlota M. Cuesta +2
Mathematics · #33C05 #35Sxx #65M70 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2001.08825

openalex publication_date 2020/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the ₂F₁ Gaussian hypergeometric function, the one-dimensional fractional Laplacian of the Higgins functions, the Christov functions, and their sine-like and cosine-like versions. After discussing the numerical difficulties in the implementation of the proposed formulas, we develop a method using variable precision arithmetic that gives accurate results.

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