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

Abstract

In this paper, we consider a class of k k -step linear multistep methods in the form (1.1) of numerical differentiation (N.D.) formulas. For each k k , we have required the property of A 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 A -stability property. It is shown that the error constant approaches that of the trapezoidal rule as k → ∞ k \to \infty and that significant reductions occur for quite modest k k . Thus, these results have significance in practical applications.