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

翻译：本文旨在展示如何利用球面上快速衰减的径向基函数拉格朗日函数，构建基于径向基函数的有效且稳定的有限差分方法（RBF-FD）。对于特定类别的偏微分方程，该方法能够为随离散精细化程度适度增长的模板提供精确的收敛性估计。