Radial basis functions method for solving three-dimensional linear Fredholm integral equations on the cubic domains

Abstract

The main purpose of this article is to describe a numerical scheme for solving three-dimensional linear Fredholm integral equations of the second kind on the cubic domains. The method is based on interpolation by radial basis functions (RBFs) based on Gauss-Legendre nodes and weights. Error analysis is presented for this method. Finally, several examples are given and numerical examples are presented to demonstrate the validity and applicability of the method.

Keywords

• three-dimensional integral equation
• radial basis functions
• collocation method
• cubic domains