  In recent years, a variety of meshless methods have been developed to solve
partial differential equations in complex domains. Meshless methods discretize
the partial differential equations over scattered points instead of grids.
Radial basis functions (RBFs) have been popularly used as high accuracy
interpolants of function values at scattered locations. In this paper, we apply
the polyharmonic splines (PHS) as the RBF together with appended polynomial and
solve the heat conduction equation in several geometries using a collocation
procedure. We demonstrate the expected exponential convergence of the numerical
solution as the degree of the appended polynomial is increased. The method
holds promise to solve several different governing equations in thermal
sciences.
