TY - JOUR
T1 - Well-Conditioned Spectral Collocation Methods for Problems in Unbounded Domains
AU - Gu , Dongqin
AU - Zhang , Chao
AU - Wang , Zhongqing
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 452
EP - 478
PY - 2020
DA - 2020/03
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0090
UR - https://global-sci.org/intro/article_detail/nmtma/15487.html
KW - Spectral collocation methods, generalized Laguerre and Hermite functions, Birkhoff interpolation, fast and stable algorithms.
AB - <p style="text-align: justify;">Based on the generalized Laguerre and Hermite functions, we construct two types of Birkhoff-type interpolation basis functions. The explicit expressions are derived, and fast and stable algorithms are provided for computing these basis functions. As applications, some well-conditioned collocation methods are proposed for solving various second-order differential equations in unbounded domains. Numerical experiments illustrate that our collocation methods are more efficient than the standard Laguerre/Hermite collocation approaches.</p>