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...
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Online Access: | http://dx.doi.org/10.1155/S0161171297000215 |
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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 |