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The aim of this paper is to show how rapidly decaying RBF Lagrange functionson the spheres can be used to create effective, stable finite differencemethods based on radial basis functions (RBF-FD). For certain classes of PDEsthis approach leads to precise convergence estimates for stencils which growmoderately with increasing discretization fineness.

Highly Localized RBF Lagrange Functions for Finite Difference Methods on Spheres