Abstract
It is well known that the order of finite difference estimates on nonuniform grids reduce dramatically, particularly when higher order derivatives are required. This paper contributes how an optimization of the order of approximation formulas can be investigated and done on such grids for a sufficiently smooth function. To generalize the idea as well as get the optimized orders, the notion of radial basis function-Hermite finite difference (RBF-HFD) approach is used. The new weighting coefficients are worked out and proved to possess higher convergence rates. Several tests are also given to demonstrate the theoretical discussions.