数值微分插值及其应用

Numerical Differential Interpolation and Its Application

中文关键词:  数值微分插值,数值调和插值,微分方程定解问题,M-阵

英文关键词:Numerical differential interpolation, Numerical harmonic interpolation, Solu-tion -determination problem of differential equations, M-Matrix,

中文摘要:

      以平面区域内偏微分方程定解问题的离散代数方程组为基础，给出了由平面区域内任意分布点上的值求整个区域中值的一种新播值方法──数值微分插值．该方法可直接推广到一维和高维空间的区域中，有较广的应用背景。

英文摘要:

      On the basis of algebraic equations of discretized solution-determination problem of partial differential equations in bounded plane domain,a new interpolation method-numeri- cal diferential interpolation(NDI) is described- Using unknown function's values on arbitrari-ly distributed points in bounded plane domain,NDI can be used to calcucate values on any points in the domain. It is also suitable for bounded domains in 1-dimension or higher di-mension space,and has wide backgrounds of applications.