We present a new technique for generating error equi-distributing meshes that satisfy both local quasi-uniformity and a preset minimal mesh spacing. This is first done in the one dimensional case by extending Kautsky and Nichols method and then in the twodimensional case by generalizing the tensor product methods to alternating curved line equidistributions. With the new meshing approach, we have achieved better accuracy in approximation using interpolatory radial basis functions. Furthermore, improved accuracy in numerical results has been obtained when the interpolatory strategy is applied to the dual reciprocity boundary element method for solving a class of linear and nonhomogeneous partial differential equation.
