Calculation of weights in finite difference formulas
Calculation of weights in finite difference formulas
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DOI：
10.1137/s0036144596322507
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发表时间：
1998-09-01
期刊：
影响因子：
10.2
通讯作者：
Fornberg, B
中科院分区：
文献类型：
--
作者：
Fornberg, B
用于确定有限差分公式中的权重的经典技术要么计算缓慢，要么在其范围内非常有限（例如，用于中心和交错近似的专门递归，用于常微分方程的Adams-Bashforth-、Adams-Moulton-和BDF-公式等）。最近的两个算法克服了这些问题。对于等间距网格，当使用Mathematica等符号语言时，可以非常方便地使用两行算法找到这些权重（在显式近似的情况下减少到一行）。对于任意间距的网格，我们描述了一个计算非常便宜的数值算法。
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.