Numerical Approximation of the Fractional Laplacian on $\mathbb R$ Using Orthogonal Families
Abstract
In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the ${}_2F_1$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.08825
- arXiv:
- arXiv:2001.08825
- Bibcode:
- 2020arXiv200108825C
- Keywords:
-
- Mathematics - Numerical Analysis;
- 33C05;
- 35Sxx;
- 65M70
- E-Print:
- 20 pages, 5 figures