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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.
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