In this paper, we present a new technique for generating error equidistributing meshes that satisfy both local quasi-uniformity and a preset minimal mesh spacing. This is firstly done in the one-dimensional case by extending the Kautsky and Nichols' method and then in the two-dimensional 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 (RBFs). Furthermore improved accuracy in numerical results have been obtained for a class of linear and non-homogeneous PDEs solved by the dual reciprocity method (DRM).
