Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains

Tao Tang*, Huifang Yuan, Tao Zhou

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

32 Citations (Scopus)


This work is concerned with spectral collocation methods for fractional PDEs in unbounded domains. The method consists of expanding the solution with proper global basis functions and imposing collocation conditions on the Gauss-Hermite points. In this work, two Hermite-type functions are employed to serve as basis functions. Our main task is to find corresponding differentiation matrices which are computed recursively. Two important issues relevant to condition numbers and scaling factors will be discussed. Applications of the spectral collocation methods to multi-term fractional PDEs are also presented. Several numerical examples are carried out to demonstrate the effectiveness of the proposed methods.
Original languageEnglish
Pages (from-to)1143-1168
Number of pages26
JournalCommunications in Computational Physics
Issue number4
Publication statusPublished - Oct 2018

Scopus Subject Areas

  • Physics and Astronomy (miscellaneous)

User-Defined Keywords

  • Fractional PDEs
  • Hermite polynomials/functions
  • Spectral collocation methods
  • Unbounded domain


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