Nontensorial generalised hermite spectral methods for PDEs with fractional Laplacian and Schrödinger operators

• Main Authors: Sheng, Changtao, Ma, Suna, Li, Huiyuan, Wang, Li-Lian, Jia, Lueling
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Generalised Hermite Polynomials; Integral Fractional Laplacian
• Online Access: https://hdl.handle.net/10356/159739
• Institution: Nanyang Technological University

In this paper, we introduce two families of nontensorial generalised Hermite polynomials/functions (GHPs/GHFs) in arbitrary dimensions, and develop efficient and accurate spectral methods for solving PDEs with integral fractional Laplacian (IFL) and/or Schrödinger operators in d. As a generalisation...