A Numerical Study of Combining RBF Interpolation and Finite Differences to Approximate Differential Operators

Abstract: This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference stencils. We compare the accuracy of this method and RBF-FD on a two-dimensional Poisson problem for standard five-point and nine-point stencils and different method parameters.