基于重心插值配点法求解变系数广义Poisson方程  

Solving the Generalized Poisson Equation with Variable Coefficient Based on Barycentric Interpolation Collocation Method

作　　者：王磊磊 WANG Lei-lei(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《兰州文理学院学报（自然科学版）》2024年第3期24-29,共6页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：提出了一种求解二维变系数广义Poisson方程的重心插值配点法,重心插值配点法是一种真正的无网格配点方法,其在计算域内不用划分网格,得出的数值解在一定误差范围内可以无限接近精确解,同时具有很好的数值稳定性.本文中的数值算例均采用重心有理插值配点法和重心Lagrange插值配点法来计算,然后通过与解析解的比较,可以得出该方法具有快速、准确和易于数值计算的优点,是一种较好的数值计算方法.A barycentric interpolation collocation method for solving the two-dimensional generalized Poisson equation with variable coefficient is proposed.The barycentric interpolation collocation method is a true meshless collocation method,which does not need to divide the grid in the calculation domain,and the numerical solution obtained can be infinitely close to the exact solution within a certain error range,and has good numerical stability.In this paper,the numerical examples are calculated using the barycentric rational interpolation collocation method and the barycentric Lagrange interpolation collocation method,and then compared with the analytical solution,it can be concluded that the method has the advantages of fast,accurate and easy numerical calculation,which is a better numerical calculation method.

关 键 词：重心有理插值 重心Lagrange插值 配点法 POISSON方程 

分 类 号：O241.82[理学—计算数学]