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On the numerical solution of differential equations with radial basis functions

Author(s): Gregory E. Fasshauer Abstract: In this paper we report on two different experiments dealing with the nu- merical solution of differential equations by radial basis functions: 1) the solution of a two-point boundary value problem; 2) the solution of a two- dimensional Poisson equation. In the second experiment we contrast a mul- tilevel collocation algorithm based on locally supported basis functions with two different direct solution approaches (one based on locally supported basis functions, the other on globally supported multiquadrics) . In both experiments the effects of a smoothing operation are studied. 1. Introduction Since their introduction in the 1970s radial basis functions (RBFs) have attracted a lot of attention from mathematicians working in the area of approximation theory. More rece... Pages: 10 Size: 1,032 kb Paper DOI: 10.2495/BT990271

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