一类含导数条件的插值问题教学研.pdfVIP

第 35 卷 第 12 期 高 师 理 科 学 刊 Vol. 35 No.12 2015 年 12 月 Journal of Science of Teachers′College and University Dec. 2015 文章编号：1007-9831（2015）12-0062-04 一类含导数条件的插值问题教学研究 杨录峰 （北方民族大学 数学与信息科学学院，宁夏 银川 750021） 摘要：从实际应用中常见的一类含导数插值条件的问题出发，推广余项校正法，构造了适合该类 插值问题的Birkhoff 插值多项式，并利用基于Birkhoff 插值的Chebyshev 谱配置点方法求解常微分 方程边值问题的近似解．与常用的谱配置点方法相比，新的谱配置点方法有两个优点：导出的线 性代数方程组的条件数与配置点个数无关；可以精确施加本质边界条件．数值实验表明，即使对 于很大的配置点个数，新的谱配置点方法仍能得到稳定的解． 关键词：Lagrange 插值；Birkhoff 插值；配置点方法；边值问题 中图分类号：O241.3∶G642.0 文献标识码：A doi：10.3969/j.issn.1007-9831.2015.12.017 Research on teaching of a class of interpolation problem with derivative conditions YANG Lu-feng （School of Mathematics and Information Science，Beifang University of Nationalities，Yinchuan 750021，China） Abstract：Generalized the conventional remainder correction approach in order to construct the Birkhoff interpolation polynomial to fit for the interpolation problem with derivative conditions，which originates in practice application．The Chebyshev collocation method based on the Birkhoff interpolation was used to solve the approximate solution of the boundary value problems of ordinary differential equations．Compared with the common collocation method，the novel collocation scheme has the following two advantages：the condition number of the linear system is independent of the number of the collocation points，and the essential boundary conditions are imposed exactly．Numerical experiments show that the stable solutions would be produce by the novel collocation method，even for the large number