On stability of nonlinear difference equations and some of their applications - Aripov, M.M.; Utebaev, D.; Utebaev, B.D.; Yarlashov, R.Sh. (Bulletin of the Karaganda University. Mathematics Series, 2024)
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.