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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
MathSciNet review: 0307441
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Abstract: In this paper, we consider a class of $ k$-step linear multistep methods in the form (1.1) of numerical differentiation (N.D.) formulas. For each $ k$, we have required the property of $ A$-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 $ A$-stability property.

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

References [Enhancements On Off] (What's this?)

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Keywords: Ordinary differential equations, numerical solution, multistep formulas, numerical stability
Article copyright: © Copyright 1972 American Mathematical Society

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