Finite difference approximations for a class of non-local parabolic equations

In this paper we study finite difference procedures for a class of parabolic equations with non-local boundary condition. The semi-implicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution of the ori...

Full description

Bibliographic Details
Main Authors:	Yanping Lin, Shuzhan Xu, Hong-Ming Yin
Format:	Article
Language:	English
Published:	Hindawi Limited 1997-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	finite difference non-local monotonicity decay stability maximum principle.
Online Access:	http://dx.doi.org/10.1155/S0161171297000215

id	doaj-1de6a0ef598b4db9b033fa05c35b69ac
record_format	Article
spelling	doaj-1de6a0ef598b4db9b033fa05c35b69ac2020-11-24T22:43:55ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120114716310.1155/S0161171297000215Finite difference approximations for a class of non-local parabolic equationsYanping Lin0Shuzhan Xu1Hong-Ming Yin2Department of Mathematical Sciences, University of Alberta Edmonton, Alberta T6G 2G1, CanadaDepartment of Mathematical Sciences, University of Alberta Edmonton, Alberta T6G 2G1, CanadaDepartment of Mathematics, University of Notre Dame, Notre Dame 46556-0398, Indiana, USAIn this paper we study finite difference procedures for a class of parabolic equations with non-local boundary condition. The semi-implicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution of the original equation, and fully-implicit scheme also possesses strict monotonicity. It is also proved that finite difference solutions approach to zero as t→∞ exponentially. The numerical results of some examples are presented, which support our theoretical justifications.http://dx.doi.org/10.1155/S0161171297000215finite differencenon-localmonotonicitydecaystabilitymaximum principle.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yanping Lin Shuzhan Xu Hong-Ming Yin
spellingShingle	Yanping Lin Shuzhan Xu Hong-Ming Yin Finite difference approximations for a class of non-local parabolic equations International Journal of Mathematics and Mathematical Sciences finite difference non-local monotonicity decay stability maximum principle.
author_facet	Yanping Lin Shuzhan Xu Hong-Ming Yin
author_sort	Yanping Lin
title	Finite difference approximations for a class of non-local parabolic equations
title_short	Finite difference approximations for a class of non-local parabolic equations
title_full	Finite difference approximations for a class of non-local parabolic equations
title_fullStr	Finite difference approximations for a class of non-local parabolic equations
title_full_unstemmed	Finite difference approximations for a class of non-local parabolic equations
title_sort	finite difference approximations for a class of non-local parabolic equations
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1997-01-01
description	In this paper we study finite difference procedures for a class of parabolic equations with non-local boundary condition. The semi-implicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution of the original equation, and fully-implicit scheme also possesses strict monotonicity. It is also proved that finite difference solutions approach to zero as t→∞ exponentially. The numerical results of some examples are presented, which support our theoretical justifications.
topic	finite difference non-local monotonicity decay stability maximum principle.
url	http://dx.doi.org/10.1155/S0161171297000215
work_keys_str_mv	AT yanpinglin finitedifferenceapproximationsforaclassofnonlocalparabolicequations AT shuzhanxu finitedifferenceapproximationsforaclassofnonlocalparabolicequations AT hongmingyin finitedifferenceapproximationsforaclassofnonlocalparabolicequations
_version_	1725693872028254208

Finite difference approximations for a class of non-local parabolic equations

Similar Items