The radial basis function differential quadrature method with ghost points

We propose a simple approach to improve the accuracy of the Radial Basis Function Differential Quadrature (RBFDQ) method for the solution of elliptic boundary value problems. While the traditional RBF-DQ method places the centers exclusively inside the domain, the proposed method expands the region for the centers allowing them to lie both inside and outside the computational domain. Furthermore, we seek an improvement to determine the shape parameter for the radial basis function by using the modified Franke's formula to find an initial search interval for the leave-one-out cross-validation method, which is a widely used method for the determination of the shape parameter. Both 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed method. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.