Semi-Implicit Difference Scheme for a Two-Dimensional Parabolic Equation with an Integral Boundary Condition

Abstract

In this paper, we consider a finite difference method for a class of two-dimensional parabolic equations with integral boundary conditions. The semi-implicit difference scheme is considered. The stability of difference 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.

Keywords:

• integral boundary condition
• semi-implicit difference scheme
• stability
• M-matrix

AMS Subject Classification:

• 65M06
• 65M12
• 65N25