@Article{CiCP-24-1409,
author = {},
title = {Solution of Cauchy Problems by the Multiple Scale Method of Particular Solutions Using Polynomial Basis Functions},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {5},
pages = {1409--1434},
abstract = {<p style="text-align: justify;">We have recently proposed a new meshless method for solving second order
partial differential equations where the polynomial particular solutions are obtained
analytically [1]. In this paper, we further extend this new method for the solution of
general two- and three-dimensional Cauchy problems. The resulting system of linear
equations is ill-conditioned, and therefore, the solution will be regularized by using
a multiple scale technique in conjunction with the Tikhonov regularization method,
while the L-curve approach is used for the determination of a suitable regularization
parameter. Numerical examples including 2D and 3D problems in both smooth and
piecewise smooth geometries are given to demonstrate the validity and applicability
of the new approach.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0187},
url = {http://global-sci.org/intro/article_detail/cicp/12483.html}
}