On using radial basis functions in a “finite difference mode” with applications to elasticity problems

Abstract

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. In particular, examples of RBF solution in the case of non-linear Karman-Fopple equations are considered.