Article

On stability of nonlinear difference equations and some of their applications

Мерсаид АриповNational University of Uzbekistan named after Mirzo Ulugbek, Tashkent, UzbekistanDauletbay UtebaevKarakalpak State University named after Berdakh, Nukus, UzbekistanB. D. UtebaevKarakalpak State University named after Berdakh, Nukus, Uzbekistan; Karakalpak branch of the Institute of Mathematics named after V.I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan, Nukus, UzbekistanR.Sh. YarlashovKarakalpak State University named after Berdakh, Nukus, Uzbekistan

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICSjournal2024en

ABI

Abstract

The issues of stability in solving nonlinear difference equations were considered. Based on a generalized difference analog of the well-known Bihari lemma, stability conditions for a trivial solution based on initial data were obtained, and an a priori estimate of stability under permanent disturbances was determined. The results were used to study the stability of solving explicit and implicit difference schemes approximating nonlinear parabolic equations.

Topics

Mathematical and Theoretical Epidemiology and Ecology Models Nonlinear Differential Equations Analysis Advanced Differential Equations and Dynamical Systems

Identifiers

DOI: 10.31489/2024m3/13-25

Citations and references

Cited by 10 references

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