@Article{NMTMA-17-1018,
author = {Gu , Dong-QinTao , Dongya and Zhang , Chao},
title = {New Log Basis Functions with a Scaling Factor and Their Applications},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2024},
volume = {17},
number = {4},
pages = {1018--1040},
abstract = {<p style="text-align: justify;">In the paper, we introduce two new classes of orthogonal functions, new
log orthogonal functions (NLOFs) and generalized new log orthogonal functions
(GNLOFs), which are based on generalized Laguerre polynomials. We construct
basis approximations analysis for the new orthogonal functions and apply them to
solve several typical differential equations. Our errors analysis and numerical results show that our methods based on the new orthogonal functions are particularly
suitable for functions which have weak singularities at one endpoint, and can obtain
exponential convergence rate, as opposed to low algebraic rates if usual orthogonal
polynomials are used.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2024-0038},
url = {http://global-sci.org/intro/article_detail/nmtma/23650.html}
}