@Article{AAMM-14-577,
author = {Chang , Jen-YiChen , Ru-Yun and Tsai , Chia-Cheng},
title = {A Comparative Study on Polynomial Expansion Method and Polynomial Method of Particular Solutions},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2022},
volume = {14},
number = {3},
pages = {577--595},
abstract = {<p style="text-align: justify;">In this study, the polynomial expansion method (PEM) and the polynomial
method of particular solutions (PMPS) are applied to solve a class of linear elliptic
partial differential equations (PDEs) in two dimensions with constant coefficients. In
the solution procedure, the sought solution is approximated by the Pascal polynomials
and their particular solutions for the PEM and PMPS, respectively. The multiple-scale
technique is applied to improve the conditioning of the resulted linear equations and
the accuracy of numerical results for both of the PEM and PMPS. Some mathematical
statements are provided to demonstrate the equivalence of the PEM and PMPS bases
as they are both bases of a certain polynomial vector space. Then, some numerical
experiments were conducted to validate the implementation of the PEM and PMPS.
Numerical results demonstrated that the PEM is more accurate and well-conditioned
than the PMPS and the multiple-scale technique is essential in these polynomial methods.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2020-0385},
url = {http://global-sci.org/intro/article_detail/aamm/20276.html}
}