Improved RBF Collocation Methods For Fourth Order Boundary Value Problems
Document Type
Article
Publication Date
5-1-2020
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
Radial basis function (RBF) collocation methods (RBFCMs) are applied to fourth order boundary value problems (BVPs). In particular, we consider the classical Kansa method and the method of approximate particular solutions (MAPS). In the proposed approach we include some so-called ghost points which are located inside and outside the domain of the problem. The inclusion of these points is shown to improve the accuracy and the stability of the collocation methods. An appropriate value of the shape parameter in the RBFs used is obtained using either the leave-one-out cross validation (LOOCV) algorithm or Franke's formula. We present and analyze the results of several numerical tests.
Publication Title
Communications in Computational Physics
Volume
27
Issue
5
First Page
1530
Last Page
1549
Recommended Citation
Chen, C.,
Karageorghis, A.,
Zheng, H.
(2020). Improved RBF Collocation Methods For Fourth Order Boundary Value Problems. Communications in Computational Physics, 27(5), 1530-1549.
Available at: https://aquila.usm.edu/fac_pubs/19107