Iterative optimization method for determining optimal shape parameter in RBF-FD method

Abstract

In this paper, we propose a novel iterative optimization method to determine the best parameter c for the Radial basis function finite difference (RBF-FD) method based on the Double Operator Error (DOE). This method is a general iterative optimization approach that can rapidly determine the optimal c for a given problem and reduce the numerical error significantly, for any type of radial basis functions (RBFs). Three numerical examples are presented to show the effectiveness and generality of the proposed method over previous methods. The relevant data and code can be found at https://github.com/hsbhc/IOM-RBF-FD.