期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1997
卷号：20
DOI：10.1155/S0161171297000215
出版社：Hindawi Publishing Corporation
摘要：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.
