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Improved RBF Collocation Methods for Fourth Order Boundary Value Problems

Improved RBF Collocation Methods for Fourth Order Boundary Value Problems
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Year:    2020

Author:    C. S. Chen, Andreas Karageorghis, Hui Zheng

Communications in Computational Physics, Vol. 27 (2020), Iss. 5 : pp. 1530–1549

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0163

Communications in Computational Physics, Vol. 27 (2020), Iss. 5 : pp. 1530–1549

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Radial basis functions Kansa method method of particular solutions collocation fourth order PDEs.

Author Details

C. S. Chen

Andreas Karageorghis

Hui Zheng

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