Splitting Schemes for Evolution Equations with a Factorized Operator

In the approximate solution of the Cauchy problem for evolution equations, the problemoperator can often be represented as a sum of simpler operators. This makes it possible toconstruct operator-difference splitting schemes, when the transition to a new level in time isprovided by solving problems f...

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Главные авторы:	Vabishchevich, P. N., Вабищевич, П. Н.
Формат:	Статья
Язык:	English
Опубликовано:	Pleiades Publishing 2024
Темы:	Evolution equation Three-level scheme Factorized operator Stability
Online-ссылка:	https://dspace.ncfu.ru/handle/123456789/29334
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spelling	ir-123456789-293342024-12-06T13:07:14Z Splitting Schemes for Evolution Equations with a Factorized Operator Vabishchevich, P. N. Вабищевич, П. Н. Evolution equation Three-level scheme Factorized operator Stability In the approximate solution of the Cauchy problem for evolution equations, the problemoperator can often be represented as a sum of simpler operators. This makes it possible toconstruct operator-difference splitting schemes, when the transition to a new level in time isprovided by solving problems for separate operator terms. We consider nonstationary problemswhose main feature is related to the representation of the problem operator as a product of theoperator by the adjoint operator. Based on the transformation of the originalequation to a system of two equations, we construct time approximations for second-orderevolution equations when the additive representation holds for the operator. Unconditional stable splitting schemes areproposed whose study is carried out with the help of general results of the theory of stability(well-posedness) of operator-difference schemes in Hilbert spaces. 2024-12-06T13:06:00Z 2024-12-06T13:06:00Z 2024 Статья Vabishchevich, P.N. Splitting Schemes for Evolution Equations with a Factorized Operator // Differential Equations. - 2024. - 60 (7). - pp. 868-876. - DOI: 10.1134/S0012266124070036 https://dspace.ncfu.ru/handle/123456789/29334 en Differential Equations application/pdf application/pdf Pleiades Publishing
institution	СКФУ
collection	Репозиторий
language	English
topic	Evolution equation Three-level scheme Factorized operator Stability
spellingShingle	Evolution equation Three-level scheme Factorized operator Stability Vabishchevich, P. N. Вабищевич, П. Н. Splitting Schemes for Evolution Equations with a Factorized Operator
description	In the approximate solution of the Cauchy problem for evolution equations, the problemoperator can often be represented as a sum of simpler operators. This makes it possible toconstruct operator-difference splitting schemes, when the transition to a new level in time isprovided by solving problems for separate operator terms. We consider nonstationary problemswhose main feature is related to the representation of the problem operator as a product of theoperator by the adjoint operator. Based on the transformation of the originalequation to a system of two equations, we construct time approximations for second-orderevolution equations when the additive representation holds for the operator. Unconditional stable splitting schemes areproposed whose study is carried out with the help of general results of the theory of stability(well-posedness) of operator-difference schemes in Hilbert spaces.
format	Статья
author	Vabishchevich, P. N. Вабищевич, П. Н.
author_facet	Vabishchevich, P. N. Вабищевич, П. Н.
author_sort	Vabishchevich, P. N.
title	Splitting Schemes for Evolution Equations with a Factorized Operator
title_short	Splitting Schemes for Evolution Equations with a Factorized Operator
title_full	Splitting Schemes for Evolution Equations with a Factorized Operator
title_fullStr	Splitting Schemes for Evolution Equations with a Factorized Operator
title_full_unstemmed	Splitting Schemes for Evolution Equations with a Factorized Operator
title_sort	splitting schemes for evolution equations with a factorized operator
publisher	Pleiades Publishing
publishDate	2024
url	https://dspace.ncfu.ru/handle/123456789/29334
work_keys_str_mv	AT vabishchevichpn splittingschemesforevolutionequationswithafactorizedoperator AT vabiŝevičpn splittingschemesforevolutionequationswithafactorizedoperator
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Splitting Schemes for Evolution Equations with a Factorized Operator

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