Title

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

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