Finite difference approximations for a class of non-local parabolic equations - Yanping Lin; Shuzhan Xu; Hong-Ming Yin (International Journal of Mathematics and Mathematical Sciences)
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.