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Abstract
The subject of this paper is the maximum principle and its application for the analysis difference schemes. To some extent, it is a survey on construction and investigation of some new classes of monotone difference schemes. The established maximum principle for derivatives has a principal meaning. The coefficient stability of difference schemes in Banach spaces is proved on the base of this principle. New results on unconditional stability of difference schemes with weights, conservative explicit‐implicit schemes (staggered schemes) are given.
Straipsnis yra apžvalginis. Jame apibendrinti rezultatai, skirti maksimumo principo naudojimui, analizuojant baigtiniu skirtumu schemu stabiluma ir konvergavima. Didžiausias demesys skiriamas sprendinio išvestiniu iverčiams. Remiantis šiuo maksimumo principo variantu irodomas kai kuriu baigtiniu skirtumu schemu koeficientinis stabilumas Banacho erdvese. Taip pat ištirtos ekonomiškos schemos, skirtos daugiamačiu uždaviniu sprendimui, ivertintas skaitinio sprendinio tikslumas, kai naudojamas netolygus diskretusis tinklas.