基于一维椭圆问题的瀑布型两层算法研究

Research on Waterfall-type Two-layer Algorithm Based on One-dimensional Elliptic Problem

通过采用牛顿二次插值作为插值算子,将粗网格(网格尺寸为4h)上的迭代解插值到细网格(网格尺寸为h)上,为其提供较好的初始值,构造了一种求解一维椭圆型问题的瀑布型两层网格法。实验结果表明该算法具有迭代步数少,计算精度高的特点,能够快速解决一维椭圆的数值问题。

In this paper,Newton quadratic interpolation is used as an interpolation operator to accurately interpolate from a coarse grid(grid size is 4h)to a refined grid(grid size is h)to provide a fine initial value and construct a waterfall-type two-layer grid method for solving one-dimensional elliptic problems.Experimental results show that the algorithm demonstrates the characteristics of fewer iteration steps and high computational accuracy,and can quickly solve the numerical problem of one-dimensional ellipse.