On the use of integrated radial basis function schemes in weighted residuals statements for elliptic problems

Abstract

In this paper, we discuss the use of integrated radial basis functions (IRBFs) in solving elliptic differential equations. Various formulations, namely point collocation, subregion collocation, Galerkin and inverse statements, are considered. IRBFs are incorporated into these formulations to represent the field variables. Numerical results indicate that this use of IRBFs leads to a considerable improvement in accuracy and convergence rate over the case of using conventional low-order polynomials.