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arXiv · 2510.06643

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

Kh. M. Shadimetov·R. S. Karimov
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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.

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Kh. M. Shadimetov, R. S. Karimov. 2025-10-08. Algorithm for constructing optimal explicit finite-difference formulas in the Hilbert space. https://arxiv.org/abs/2510.06643

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