A priori estimates expressing continuous dependence of the solution of a first order evolutionary equation in Hubert space on initial condition, right hand side and operator perturbations are obtained in time–integral norms. Analogous results hold for corresponding finite difference schemes.
Santrauka. Darbe tiriamas pirmosios eilės nestacionarių diferencialinių lygčių, apibrėžtų Huberto erdvėse, stabilumas pradinės sąlygos, laisvųjų narių ir operatoriaus koeficientų atžvilgiu. Stabilumo įverčiai įrodomi integralinėse laiko atžvilgiu normose. Analogiški rezultatai gauti ir baigtinių skirtumų schemoms. Įrodyti stipraus stabilumo įverčiai, kai modifikuojami lygties operatorius ir pradinė sąlyga. Teoriniai rezultatai pritaikyti vienmačiam šilumos laidumo uždaviniui ir jį aproksimuojančiai baigtinių skirtumų schemai.
Matus, P. P., & Jovanović, B. S. (1999). Coefficient stability of operator–difference schemes. Mathematical Modelling and Analysis, 4(1), 135-146. https://doi.org/10.3846/13926292.1999.9637118
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