Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem...

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Main Author:	Yubin Yan
Format:	Article
Language:	English
Published:	Hindawi Limited 2005-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/IJMMS.2005.523

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spelling	doaj-3f02aab0e1474e7f8a89661d75e427242020-11-24T22:48:53ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005452353610.1155/IJMMS.2005.523Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equationsYubin Yan0Department of Mathematics, The University of Manchester, Manchester M13 9PL, UKA smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.http://dx.doi.org/10.1155/IJMMS.2005.523
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yubin Yan
spellingShingle	Yubin Yan Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations International Journal of Mathematics and Mathematical Sciences
author_facet	Yubin Yan
author_sort	Yubin Yan
title	Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations
title_short	Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations
title_full	Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations
title_fullStr	Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations
title_full_unstemmed	Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations
title_sort	smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2005-01-01
description	A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.
url	http://dx.doi.org/10.1155/IJMMS.2005.523
work_keys_str_mv	AT yubinyan smoothingpropertiesinmultistepbackwarddifferencemethodandtimederivativeapproximationforlinearparabolicequations
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Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

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