Infinitely Smooth Polyharmonic RBF Collocation Method for Numerical Solution of Elliptic PDEs

In this article, a novel infinitely smooth polyharmonic radial basis function (PRBF) collocation method for solving elliptic partial differential equations (PDEs) is presented. The PRBF with natural logarithm piecewise in the conventional governing equations. We converted into an using source points collocated outside domain to ensure that distance was always greater than zero avoid singularity of PRBF. Accordingly, and its derivatives PDEs were continuous. seismic wave propagation problem, groundwater flow unsaturated contamination problem investigated reveal robustness proposed Comparisons carried out as well. results illustrate approach could provide more accurate solutions PRBF, even optimal order. Furthermore, we also demonstrated techniques designed deal original are no longer required.