LAUSR

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-oneout cross validation (LOOCV) algorithm or Franke’s formula. We present and analyze the results of several numerical tests. AMS subject classifications: 65N35, 65N99