TY - JOUR
T1 - Improved RBF Collocation Methods for Fourth Order Boundary Value Problems
AU - S. Chen , C.
AU - Karageorghis , Andreas
AU - Zheng , Hui
JO - Communications in Computational Physics
VL - 5
SP - 1530
EP - 1549
PY - 2020
DA - 2020/03
SN - 27
DO - http://doi.org/ 10.4208/cicp.OA-2019-0163
UR - https://global-sci.org/intro/article_detail/cicp/15768.html
KW - Radial basis functions, Kansa method, method of particular solutions, collocation, fourth order PDEs.
AB - <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>