Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Abstract

Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions.