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

Pelios, A.; Klopfenstein, R. W.

doi:10.1090/S0025-5718-1972-0307441-2

Minimal error constant numerical differentiation (N.D.) formulas
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by A. Pelios and R. W. Klopfenstein PDF

Math. Comp. 26 (1972), 467-475 Request permission

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.

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