Calculation of weights in finite difference formulas

被引：278

作者：

Fornberg, B ^{[1
]}

机构：

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

来源：

SIAM REVIEW | 1998年 / 40卷 / 03期

关键词：

finite differences; weights; interpolation; linear multistep methods;

D O I：

10.1137/S0036144596322507

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The classical techniques for determining weights in finite difference formulas were either computationally slow or very limited in their scope (e.g., specialized recursions for centered and staggered approximations, for Adams-Bashforth-, Adams-Moulton-, and BDF-formulas for ODEs, etc.). Two recent algorithms overcome these problems. For equispaced grids, such weights can be found very conveniently with a two-line algorithm when using a symbolic language such as Mathematica (reducing to one line in the case of explicit approximations). For arbitrarily spaced grids, we describe a computationally very inexpensive numerical algorithm.

引用

页码：685 / 691

页数：7