求解二维Poisson方程的重心有理插值配点法  

Collocation Method with Barycentric Rational Interpolation for Poisson Equations

作　　者：吴君 张学莹[1] WU Jun, ZHANG Xue-ying(College of Science, Hohai University, Nanjng 211100, Chin)

机构地区：[1]河海大学理学院

出　　处：《数学的实践与认识》2018年第17期238-245,共8页Mathematics in Practice and Theory

基　　金：江苏省自然科学基金(BK20160853);教育部留学回国人员科研启动基金(20145003412);中央高校科研业务费基金(2018B43814)

摘　　要：首先介绍了重心Lagrange插值法,然后通过改变重心Lagrange插值法的插值权函数,重点给出了重心有理插值的具体形式.基于等距节点和Chebyshev节点这两类插值节点,利用重心有理插值配点法求解了二维Poisson方程,并比较了采用上述两种插值节点时的计算精度.数值算例表明,重心有理插值配点法具有稳定性好,计算精度高和程序编写简单的特点.In this paper, we first introduces the barycentric Lagrange interpolation method, then we focus on giving the specific form of the barycentric rational interpolation by changing the interpolation weight function of the barycentric Lagrange interpolation method. Based on equidistant nodes and Chebyshev nodes, we have solved two-dimension Poisson equation by using collocation method with barycentric rational interpolation, and compared the calculation precision with the above two kinds of nodes. The numerical examples show that the collocation method with barycentric rational interpolation has the characteristics of better stability, high accuracy and simple program.

关 键 词：POISSON方程 重心有理插值 配点法 

分 类 号：O241.3[理学—计算数学]