Finite difference approximations for a class of non-local parabolic equations

Yanping Lin, Shuzhan Xu and Hong-Ming Yin

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-17

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 → ∞ exponentially. The numerical results of some examples are presented, which support our theoretical justifications.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:191924

DOI: 10.1155/S0161171297000215

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