On comparing Adams and natural spline multistep formulas

Hill, David R.

doi:10.1090/S0025-5718-1975-0375781-X

On comparing Adams and natural spline multistep formulas
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Math. Comp. 29 (1975), 741-745 Request permission

Abstract:

This paper presents two techniques for the comparison of Adams formulas and methods based on natural splines. A rigorous foundation to the claim that a pth order natural spline formula produces better results than a pth order Adams method, but not quite as good as a $(p + 1)$st order Adams formula is given for $p = 2,3,4$, which suggests the general case.

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