Compact approximation stencils based on integrated flat radial basis functions

This paper presents improved ways of constructing compact integrated radial basis function (CIRBF) stencils, based on extended precision, definite integrals, higher-order IRBFs and minimum number of derivative equations, to enhance their performance over large values of the RBF width. The proposed approaches are numerically verified through second-order linear differential equations in one and two variables. Significant improvements in the matrix condition number, solution accuracy and convergence rate with grid refinement over the usual approaches are achieved.