2018/12/18 by Kailai Xu, Xu, Kailai, Eric Darve +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1812.08325
openalex publication_date 2018/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls. The method is based on the explicit formulation of the eigenfunctions and eigenvalues of the fractional Laplacian in the unit balls under the weighted L2 space. The resulting method enjoys spectral accuracy for all fractional index α∈ (0,2) and is computationally efficient due to the orthogonality of the basis functions. We also proposed a numerical integration strategy for computing the coefficients. Numerical examples in 2D and 3D are shown to demonstrate the effectiveness of the proposed methods.