几种数值插值方法的试验比较

该文首先引进３种精度较高的边界条件，借助于Ｓｐｌｉｎｅ函数，近似计算离散网格上的一阶空间微商，并通过数值试验进行比较，然后用Ｌａｇｒａｎｇｉａｎ、Ｓｐｌｉｎｅ和Ｈｅｒｍｉｔｅ方法对不同相对位置的插值点作插值计算，并给出一套较为简单适用的Ｈｅｒｍｉｔｅ方案计算公式。结果表明，这３类插值方法都能达到一定的精度，但其中以取周期性边界条件，用Ｈｅｒｍｉｔｅ方法算得的插值函数最为精确，其误差约为采用二阶或三

Experimental Comparisons Among Several Numerical interpolation Methods

Three higher-accurate boundary conditions is introduced. The first-order spacial differential is calculated by using the Spline function,and a set of simpler calculating formulation of the Hermite method is presented. Comparisons of the interpolation errors among the Lagrangian, the Spline and the Hermite schemes for different locations of the interpolation points are made. The results show that although these schemes have given accuracies to some extent,the error of the Hermite method with periodic boundary condition is around one fourth or a half of the errors of other boundary conditions, and is about one order of magnitude smaller than that of the Lagrangian technique.