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Calculation of Weights in Finite Difference Formulas

B. Fornberg
Journal / Anthology

SIAM Review
Year: 1998
Volume: 40
Issue: 3
Page range: 685-691

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-lined 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.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations