Algorithm for constructing optimal explicit finite-difference formulas in the Hilbert space

Abstract

This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem of optimizing finite-difference formulas in the space $W_2^{\left(m,m-1\right)}\left(0,1\right)$. Here, representations of optimal coefficients of explicit finite-difference formulas of the Adams type on classes $W_2^{\left(m,m-1\right)}\left(0,1\right)$ for any $m\ge 3$ will be found.

The authors are requested to retract this article to make substantial changes. A revised version will be submitted later