Finite Difference Approximations for a Class of
Non-local Parabolic Equations
ABSTRACT
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 $t \rr \infty$
exponentially.
The numerical results of some examples are presented , which support
our theoretical justifications.