TY - JOUR
T1 - Polynomial Particular Solutions for the Solutions of PDEs with Variables Coefficients
AU - Lu , Jun
AU - Yu , Hao
AU - Lin , Ji
AU - Dangal , Thir
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1247
EP - 1260
PY - 2018
DA - 2018/07
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2018-0016
UR - https://global-sci.org/intro/article_detail/aamm/12597.html
KW - Polynomial particular solutions, variable coefficients, multiple scale methods, collocation
approach, method of approximate particular solutions.
AB - <p style="text-align: justify;">The closed-form particular solutions with polynomial basis functions for
general partial differential equations (PDEs) with constant coefficients have been derived
and applied for solving various kinds of problems in the context of the method
of approximate particular solutions (MAPS). In this paper, we propose to extend the
above-mentioned method to PDEs with variable coefficients by the substituting and
adding-back technique. Since the linear system derived from the polynomial particular
solutions is notoriously ill-conditioned, the multiple scale method is applied to
alleviate this difficulty. To validate our proposed method, four numerical examples
are considered and compared with those obtained by the MAPS using the radial basis
functions.</p>