Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory

We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of the solution. The main problems of the approximate solution of such nonlocal problems are due to the necessity to work wit...

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Главные авторы:	Vabishchevich, P. N., Вабищевич, П. Н.
Формат:	Статья
Язык:	English
Опубликовано:	2023
Темы:	Cauchy problem Finite-dimensional Hilbert space Volterra integral equations Ordinary differential equations
Online-ссылка:	https://dspace.ncfu.ru/handle/20.500.12258/23464
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id	ir-20.500.12258-23464
record_format	dspace
spelling	ir-20.500.12258-234642025-02-11T12:58:09Z Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory Vabishchevich, P. N. Вабищевич, П. Н. Cauchy problem Finite-dimensional Hilbert space Volterra integral equations Ordinary differential equations We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of the solution. The main problems of the approximate solution of such nonlocal problems are due to the necessity to work with the approximate solution for all previous time moments. We propose a transformation of the first-order integrodifferential equation to a system of local evolutionary equations. We use the approach known in the theory of Volterra integral equations with an approximation of the difference kernel by the sum of exponents. We formulate a local problem for a weakly coupled system of equations with additional ordinary differential equations. We have given estimates of the stability of the solution by initial data and the right-hand side for the solution of the corresponding Cauchy problem. The primary attention is paid to constructing and investigating the stability of two-level difference schemes, which are convenient for computational implementation. The numerical solution of a two-dimensional model problem for the evolution equation of the first order, when the Laplace operator conditions the dependence on spatial variables, is presented. 2023-05-11T12:41:33Z 2023-05-11T12:41:33Z 2023 Статья Vabishchevich, P.N. Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory // Journal of Computational Physics. - 2023. - 422, № 114887. - DOI: 10.1016/j.cam.2022.114887 http://hdl.handle.net/20.500.12258/23464 en Journal of Computational Physics application/pdf application/pdf
institution	СКФУ
collection	Репозиторий
language	English
topic	Cauchy problem Finite-dimensional Hilbert space Volterra integral equations Ordinary differential equations
spellingShingle	Cauchy problem Finite-dimensional Hilbert space Volterra integral equations Ordinary differential equations Vabishchevich, P. N. Вабищевич, П. Н. Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory
description	We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of the solution. The main problems of the approximate solution of such nonlocal problems are due to the necessity to work with the approximate solution for all previous time moments. We propose a transformation of the first-order integrodifferential equation to a system of local evolutionary equations. We use the approach known in the theory of Volterra integral equations with an approximation of the difference kernel by the sum of exponents. We formulate a local problem for a weakly coupled system of equations with additional ordinary differential equations. We have given estimates of the stability of the solution by initial data and the right-hand side for the solution of the corresponding Cauchy problem. The primary attention is paid to constructing and investigating the stability of two-level difference schemes, which are convenient for computational implementation. The numerical solution of a two-dimensional model problem for the evolution equation of the first order, when the Laplace operator conditions the dependence on spatial variables, is presented.
format	Статья
author	Vabishchevich, P. N. Вабищевич, П. Н.
author_facet	Vabishchevich, P. N. Вабищевич, П. Н.
author_sort	Vabishchevich, P. N.
title	Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory
title_short	Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory
title_full	Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory
title_fullStr	Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory
title_full_unstemmed	Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory
title_sort	approximate solution of the cauchy problem for a first-order integrodifferential equation with solution derivative memory
publishDate	2023
url	https://dspace.ncfu.ru/handle/20.500.12258/23464
work_keys_str_mv	AT vabishchevichpn approximatesolutionofthecauchyproblemforafirstorderintegrodifferentialequationwithsolutionderivativememory AT vabiŝevičpn approximatesolutionofthecauchyproblemforafirstorderintegrodifferentialequationwithsolutionderivativememory
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Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory

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