A Simplified Radial Basis Function Method with Exterior Fictitious Sources for Elliptic Boundary Value Problems

In this article, we propose a simplified radial basis function (RBF) method with exterior fictitious sources for solving elliptic boundary value problems (BVPs). Three RBFs, including Gaussian, multiquadric (MQ), and inverse (IMQ) without the shape parameter, are adopted in study. With consideration of many outside domain, distance RBF is always greater than zero, such that can remove parameter from RBFs. Additionally, MQ, IMQ RBFs their derivatives governing equation smooth nonsingular. Comparative analysis conducted three different collocation types, conventional uniform centers, randomly sources. Numerical examples BVPs two dimensions carried out. The results demonstrate proposed significantly improve accuracy, especially Laplace equation. Furthermore, exhibit simplicity finding optimum parameter.