Article

On a Method for Constructing Optimal Difference Formulas Using Discrete Operators with Variable Coefficients

Kholmat ShadimetovComputational Mathematics Laboratory, V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 4b University Str., Tashkent 100174, UzbekistanShermamat EsanovComputational Mathematics Laboratory, V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 4b University Str., Tashkent 100174, Uzbekistan

Algorithmsjournal2026en

ABI

Abstract

This paper deals with the problem of constructing optimal difference formulas in the Hilbert space H2m0,1 through Sobolev’s method. Firstly, Sobolev’s method of construction of optimal difference formulas in the Hilbert space H2m0,1, which is based on the discrete analogue Lhβ, is described. Secondly, a discrete analogue Lhβ of differential operator d2dx2+2sgnxddx+11−d2dx2m−2 having variable coefficients is contructed. Thirdly, for m=2 the optimal difference formula is obtained. Finally, at the end of the paper, we present some numerical results, which serves to confirm the numerical convergence of the optimal difference formula.

Topics

Differential Equations and Boundary Problems Diverse Research Studies Overview Fractional Differential Equations Solutions

Identifiers

DOI: 10.3390/a19020163

Citations and references

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