High accurate finite differences based on RBF interpolation and its application in solving differential equations
The aim of the paper is to develop highly accurate finite difference (FD) approximations to solve differential equations. The tool to be used is the radial basis function (RBF) interpolation with zero degree precision. The Lagrange form of the RBF interpolation is used to avoid the problem of matrix inversion that would arise otherwise. The authors focus on the analysis of truncation errors of two RBF-FD schemes and apply these schemes to three different kinds of differential equations. There is some care needed (and discussed) in how the differential equations are applied to estimate the parameter \(\epsilon\) of the method. The authors conclude with some numerical examples and an implementation discussion.
scientific article; zbMATH DE number 6945495