EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS

We have considered the Cauchy problem for a first-order evolutionary equation with fractional powers of an operator. Such nonlocal mathematical models are used, for example, to describe anomalous diffusion processes. We want the transition to a new level in time to be solved usual problems. Computat...

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Главные авторы:	Vabishchevich, P. N., Вабищевич, П. Н.
Формат:	Статья
Язык:	English
Опубликовано:	2023
Темы:	Stability of operator-difference schemes Evolutionary equation Exponent splitting scheme Fractional powers of an operator Rational approximation
Online-ссылка:	https://dspace.ncfu.ru/handle/20.500.12258/24071
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id	ir-20.500.12258-24071
record_format	dspace
spelling	ir-20.500.12258-240712025-02-11T12:12:14Z EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS Vabishchevich, P. N. Вабищевич, П. Н. Stability of operator-difference schemes Evolutionary equation Exponent splitting scheme Fractional powers of an operator Rational approximation We have considered the Cauchy problem for a first-order evolutionary equation with fractional powers of an operator. Such nonlocal mathematical models are used, for example, to describe anomalous diffusion processes. We want the transition to a new level in time to be solved usual problems. Computational algorithms are constructed based on some approximations of operator functions. Currently, when solving stationary problems with fractional powers of an operator, the most attention is paid to rational approximations. In the approximate solution of nonstationary problems, we come to equations with an additive representation of the problem operator. Additive-operator schemes are constructed by using different variants of splitting schemes. In the present work, the time approximations are based on approximations of the transition operator by the product of exponents. We use exponent splitting schemes of the first and second-order accuracy. The results of numerical experiments for a two-dimensional model problem with fractional powers of the elliptic operator are presented. 2023-07-07T09:53:05Z 2023-07-07T09:53:05Z 2023 Статья Vabishchevich, P.N. EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS // International Journal of Numerical Analysis and Modeling. - 2023. - 20(3), pp. 371–390. - DOI: 10.4208/ijnam2023-1015 http://hdl.handle.net/20.500.12258/24071 en International Journal of Numerical Analysis and Modeling application/pdf application/pdf
institution	СКФУ
collection	Репозиторий
language	English
topic	Stability of operator-difference schemes Evolutionary equation Exponent splitting scheme Fractional powers of an operator Rational approximation
spellingShingle	Stability of operator-difference schemes Evolutionary equation Exponent splitting scheme Fractional powers of an operator Rational approximation Vabishchevich, P. N. Вабищевич, П. Н. EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS
description	We have considered the Cauchy problem for a first-order evolutionary equation with fractional powers of an operator. Such nonlocal mathematical models are used, for example, to describe anomalous diffusion processes. We want the transition to a new level in time to be solved usual problems. Computational algorithms are constructed based on some approximations of operator functions. Currently, when solving stationary problems with fractional powers of an operator, the most attention is paid to rational approximations. In the approximate solution of nonstationary problems, we come to equations with an additive representation of the problem operator. Additive-operator schemes are constructed by using different variants of splitting schemes. In the present work, the time approximations are based on approximations of the transition operator by the product of exponents. We use exponent splitting schemes of the first and second-order accuracy. The results of numerical experiments for a two-dimensional model problem with fractional powers of the elliptic operator are presented.
format	Статья
author	Vabishchevich, P. N. Вабищевич, П. Н.
author_facet	Vabishchevich, P. N. Вабищевич, П. Н.
author_sort	Vabishchevich, P. N.
title	EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS
title_short	EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS
title_full	EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS
title_fullStr	EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS
title_full_unstemmed	EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS
title_sort	exponent splitting schemes for evolution equations with fractional powers of operators
publishDate	2023
url	https://dspace.ncfu.ru/handle/20.500.12258/24071
work_keys_str_mv	AT vabishchevichpn exponentsplittingschemesforevolutionequationswithfractionalpowersofoperators AT vabiŝevičpn exponentsplittingschemesforevolutionequationswithfractionalpowersofoperators
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EXPONENT SPLITTING SCHEMES FOR EVOLUTION EQUATIONS WITH FRACTIONAL POWERS OF OPERATORS

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