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The maximum principle and its application for the analysis of difference schemes

    A. P. Matus Affiliation
    ; P. P. Matus Affiliation

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.


Maksimumo principas ir jo naudojimas baigtinių skirtumų schemų analizėje


Santrauka


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.


First Published online: 14 Oct 2010

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How to Cite
Matus, A. P., & Matus, P. P. (2001). The maximum principle and its application for the analysis of difference schemes. Mathematical Modelling and Analysis, 6(2), 289-299. https://doi.org/10.3846/13926292.2001.9637168
Published in Issue
Dec 15, 2001
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