Semi-implicit difference scheme for a two-dimensional parabolic equation with an integral boundary condition

Abstract

In this paper, we consider a nite dierence method for a class of two-dimensional parabolic equations with integral boundary conditions. The semi-implicit dierence scheme is considered. The stability of dierence scheme is proved using the properties of the M-matrices, particularly, the regular splitting of an M-matrix. The numerical results of some examples are presented, that approve our theoretical investigations.