Work

Optimal interpolation formulas in the Sobolev space of periodic functions W̃2(m)(T1)

Year: 2026

Type: article

Abstract: The problem of finding the extremal function of an interpolation formula and of evaluating the norm of the error functional in the Sobolev space was first posed by S.L.Sobolev. In that work, the extremal function of the interpolation formula was obtained explicitly in the Sobolev space whose generalized derivatives of order $m$ are square-integrable. The present paper considers a new optimal interpolation formula in the Sobolev space: using the discrete analog of the differential operator, we obtain the optimal coefficients of the interpolation formula for an arbitrary $m$, and the norm of the error functional is computed. Integration of the interpolant leads to a quadrature formula; three numerical examples confirm the theoretical order of convergence.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2026.100786

Authors: Kholmat Shadimetov, Khurshidjon Khayatov

Institutions: Tashkent State Transport University, Academy of Sciences Republic of Uzbekistan, Bukhara State University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,770

OpenAlex ID: W7223382654

FWCI:

Cites: 19

Cited by:

Related to: 10