On the numerical solution of differential equations with radial basis functions

In this paper we report on two different experiments dealing with the numerical solution of differential equations by radial basis functions: 1) the solution of a two-point boundary value problem; 2) the solution of a twodimensional Poisson equation. In the second experiment we contrast a multilevel 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.

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