带自然边界条件多元多项式样条插值及微分方程数值解  

Multivariate polynomial spline interpolation with natural boundary conditions and numerical solution of differential equation

作　　者：徐应祥[1] 

机构地区：[1]中山大学新华学院,广东广州510520

出　　处：《合肥工业大学学报（自然科学版）》2015年第9期1281-1286,共6页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(10871160)

摘　　要：文章考虑对d维散乱数据的一种带自然边界条件多元多项式样条插值问题,在使目标泛函极小的情况下,用Hilbert空间样条函数方法得出插值解可表示为一个多元多项式,其表示形式简单,且系数可由系数矩阵对称的线性方程组确定,最后将其应用于求微分方程数值解,并举例说明了方法的有效性。A kind of interpolation for scattered data of d‐D by multivariate polynomial spline with natu‐ral boundary conditions is considered .Using the spline ways of Hilbert space ,the interpolation solu‐tion is constructed as a multivariate polynomial with simple expression .It makes the given objective function minimized and its coefficients be decided by a linear system with symmetry coefficient matrix . Finally ,the interpolation spline is used to solve differential equations and get the numerical solutions . Some examples are presented to illustrate the effectiveness of the method .

关 键 词：散乱数据 自然样条 数值解 

分 类 号：O242.2[理学—计算数学] TP391.7[理学—数学]