A RBF-HFD scheme for numerical solution of partial differential equations

Radial basis function - finite difference formulas (RBF-FD) have received much attention in recent years due to their high accuracy, well conditioning and simplicity in implementation on irregular and non-rectangular domaines. To improve the accuracy of RBF-FD without increasing the stencil size the RBF-HFD have been proposed. This paper presents a new compact Hermite radial basis finite difference scheme RBF-HFD for approximation of partial differential equations. We obtain analytical weights and truncation errors of these formulas for first derivative, and second derivative. Numerical results show well the efficiency of the introduced method.