中文摘要：

点源热传导问题和集中力作用梁变形问题的数学模型中,源项为奇异的Delta函数.采用数值稳定性好的重心型插值近似未知函数,利用Delta函数与Heaviside函数的导数关系以及Delta函数的积分筛选性,建立求解含有奇异源项问题的重心插值配点法和重心插值Galerkin法.通过数值算例比较两个方法的有效性和计算精度.

英文摘要：

Mathematical models for heat conduction with point source and beam bending with concentrated force include singular Delta function in the source term.Barycentric Lagrange 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.