IOM-RBF-FD

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

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 Double Operator Error (DOE). This method is a general iterative optimization approach which 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.