@Article{CiCP-27-5,
author = {S., Chen, C. and Karageorghis, Andreas and Zheng, Hui},
title = {Improved RBF Collocation Methods for Fourth Order Boundary Value Problems},
journal = {Communications in Computational Physics},
year = {2020},
volume = {27},
number = {5},
pages = {1530--1549},
abstract = {<p style="text-align: justify;"><span style="font-family: 微软雅黑, ">Radial basis function (RBF) collocation methods (RBFCMs) are applied to&nbsp;fourth order boundary value problems (BVPs). In particular, we consider the classical&nbsp;Kansa method and the method of approximate particular solutions (MAPS). In the&nbsp;proposed approach we include some so-called ghost points which are located inside&nbsp;and outside the domain of the problem. The inclusion of these points is shown to&nbsp;improve the accuracy and the stability of the collocation methods. An appropriate&nbsp;value of the shape parameter in the RBFs used is obtained using either the leave-one-out cross validation (LOOCV) algorithm or Franke&#39;s formula. We present and analyze&nbsp;the results of several numerical tests.</span></p>},
issn = {1991-7120},
doi = {https://doi.org/ 10.4208/cicp.OA-2019-0163},
url = {https://global-sci.com/article/79802/improved-rbf-collocation-methods-for-fourth-order-boundary-value-problems}
}