The Global Error Estimate For Solving PDE Numerically By Hermite-Birkhoff Interpolation With Radial Basis Functions

The Hermit-Birkhoff interpolation with radial basis functions is an effective method in solving partial differential equations numerically. Present studies on the local error estimates of this method see the interior data and the boundary data density as one. These estimate cannot reflect the different effects of the two kind of data on the error.This paper, aimed at getting a global error estimate of the method which can reflect the different effects of the two kinds of data on the error, considers the two types of data separately and defines two kinds of data density. It includes three parts. The first part briefly introduces the basic knowledge of radial basis interpolation, consisting of the definition of radial function, the formulae of radial basis interpolation, Kansa's method and the Hermite-Birkhoff interpolation with radial basis functions. In the following part, some researchers'studies in local error estimates of the radial basis interpolation are introduced. The third part is the main part of this paper, gives a detailed discussion on the Poisson equation with Dirichlet boundary condition, and derives a global esti-mate for solving the special equation.by the Hermite-Birkhoff interpolation with radial basis functions.