山东建筑大学学报2017，Vol.32Issue(3)：245-250,6.
梁方程降阶计算的重心插值配点法
Barycentric interpolation collocation method based on depression of order for solving beam equations
摘要
Abstract
When the beam equations are solved by barycentric interpolation collocation method,computational accuracy will decline gradually as the number of nodes increases.The research on barycentric interpolation collocation method based on depression of order,can provide the new method that has a good numerical stability and high computational accuracy for beam equations.Based on barycentric Lagrange interpolation and its differential matrices,the formula of barycentric interpolation collocation method based on depression of order is derived.Numerical examples are given to verify the effectiveness of the proposed method.The result shows that the computational accuracy of depression of order method remains the range of 10-10 ～ 10-12 as the number of nodes increases.When the beam equations with simply supported ends are solved,the computational accuracy of the two-step depression of order method is higher than the one-step depression of order method.The condition number of the direct method is close to 7th power of the number of nodes,and the condition number of one-step depression of order method is close to 4th power of the number of nodes.The depression of order method can effectively reduce the condition number of computing matrix such that improves the computational accuracy.By applying the computational formula with matrix-vector form,the program is easy to write and the computational efficiency of barycentric interpolation collocation method can be improved remarkably.关键词
梁方程/降阶法/重心Lagrange插值/配点法Key words
beam equations/depression of order method/barycentric Lagrange interpolation/collocation method分类
数理科学引用本文复制引用
徐子康,王兆清,孙浩森,李金..梁方程降阶计算的重心插值配点法[J].山东建筑大学学报,2017,32(3):245-250,6.基金项目
国家自然科学基金面上项目(51379113) （51379113）
国家自然科学基金项目(11471195) （11471195）
山东省自然科学基金重点项目(ZR2016JL006) （ZR2016JL006）
