International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 147-163
Finite difference approximations for a class of non-local parabolic equations
1Department of Mathematical Sciences, University of Alberta Edmonton, Alberta T6G 2G1, Canada
2Department of Mathematics, University of Notre Dame, Notre Dame 46556-0398, Indiana, USA
Received 4 October 1994
Copyright © 1997 Yanping Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 exponentially. The
numerical results of some examples are presented, which support our theoretical justifications.