Using radial basis functions in a "finite difference mode"

A way of using RBF as the basis for PDE's solvers is presented, its essence being constructing approximate formulas for derivatives discretizations based on RBF interpolants with local supports similar to stencils in finite difference methods. Numerical results for different types of elasticity equations showing reasonable accuracy and good h-convergence properties of the technique are presented. Applications of the technique to problems with non-self-adjoint operators (like those for the Navier-Stokes equations) are also considered.