  Conventionally, piecewise polynomials have been used in the boundary elements
method (BEM) to approximate unknown boundary values. Since infinitely smooth
radial basis functions (RBFs) are more stable and accurate than the polynomials
for high dimensional domains, the unknown values are approximated by the RBFs
in this paper. Therefore, a new formulation of BEM, called radial BEM, is
obtained. To calculate singular boundary integrals of the new method, we
propose a new distribution for boundary source points that removes singularity
from the integrals. Therefore, the boundary integrals are calculated precisely
by the standard Gaussian quadrature rule (GQR) with n = 16 quadrature nodes.
Several numerical examples are presented to check the efficiency of the radial
BEM versus standard BEM and RBF collocation method for solving partial
differential equations (PDEs). Analytical and numerical studies presented in
this paper admit the radial BEM as a perfect version of BEM which will enrich
the contribution of BEM and RBFs in solving PDEs, impressively.
