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.
Categories: math.NA cs.NA