关键词: 奇异源, 重心Lagrange插值, 重心插值配点法, 重心插值Galerkin法

Abstract: Mathematical models for heat conduction with point source and beam bending with concentrated force include singular Delta function in the source term.Barycentric Lngrange interpolation is used to approximate unknown functions.Barycentric interpolation collocation method and barycentric interpolation Galerkin method for singular source problems are presented using relation between delta function and derivative of Heaviside function and integrated property of delta function.Formulations of the method are given in detail.Two one-dimensional examples and a two-dimensional example are shown.It demonstrates effectiveness and precision of the methods.

Key words: singular source, barycentric Lagrange interpolation, barycentric interpolation coUocation method, barycentric interpolation Galerkin method