AN ALTERNATING DIRECTION IMPLICIT DIFFERENCE SCHEME FOR TWO DIMENSIONAL SEMILINEAR REACTION-DIFFUSION EQUATION
二维半线性反应扩散方程的交替方向隐格式

The purpose of this work is to study difference method for a two dimensional semi- linear reaction-diffusion equation.An alternating direction implicit difference scheme is constructed.The proposed scheme is a two-level and linearization scheme.Using discrete energy estimates,existence and uniqueness of difference scheme are proved and convergence and stability of difference scheme in discrete H~1 norm are also obtained.Two numerical examples are presented and compared with the exact analytical solution for its order of convergence.