TY - JOUR
T1 - Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains
AU - Tao Tang, Huifang Yuan & Tao Zhou
JO - Communications in Computational Physics
VL - 4
SP - 1143
EP - 1168
PY - 2018
DA - 2018/06
SN - 24
DO - http://doi.org/10.4208/cicp.2018.hh80.12
UR - https://global-sci.org/intro/article_detail/cicp/12322.html
KW - Fractional PDEs, Hermite polynomials/functions, unbounded domain, spectral collocation methods.
AB - <p style="text-align: justify;">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.</p>