Minimal error constant numerical differentiation (N.D.) formulas

Authors:
A. Pelios and R. W. Klopfenstein

Journal:
Math. Comp. **26** (1972), 467-475

MSC:
Primary 65D25

DOI:
https://doi.org/10.1090/S0025-5718-1972-0307441-2

MathSciNet review:
0307441

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we consider a class of -step linear multistep methods in the form (1.1) of numerical differentiation (N.D.) formulas. For each , we have required the property of -stability which implies at most second order for the associated operator. Among such second-order operators, the parameters of the formulas have been selected to minimize the error constant consistent with the -stability property.

It is shown that the error constant approaches that of the trapezoidal rule as and that significant reductions occur for quite modest . Thus, these results have significance in practical applications.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0307441-2

Keywords:
Ordinary differential equations,
numerical solution,
multistep formulas,
numerical stability

Article copyright:
© Copyright 1972
American Mathematical Society