@Article{AAMM-10-5,
author = {Zhengzhi, Li and Watson, Daniel and Ming, Li and Thir, Dangal},
title = {The LMAPS Using Polynomial Basis Functions for Near-Singular Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {5},
pages = {1090--1102},
abstract = {<p style="text-align: justify;">In this paper, we combine the Local Method of Approximate Particular Solutions
(LMAPS) with polynomial basis functions to solve near-singular problems. Due
to the unique feature of the local approach, the LMAPS is capable of capturing the
rapid variation of the solution. Polynomial basis functions can become very unstable
when the order of the polynomial becomes large. However, since the LMAPS is a local
method, the order does not need to be very high; an order of 5 can achieve sufficient
accuracy. In order to show the effectiveness of the LMAPS using polynomial basis
functions for solving near singular problems, we compare the results with the LMAPS
using radial basis functions (RBFs). The advantage of using polynomials as a basis
rather than RBFs is that finding an appropriate shape parameter is not necessary.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2017-0288},
url = {https://global-sci.com/article/73214/the-lmaps-using-polynomial-basis-functions-for-near-singular-problems}
}