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半线性; 反应扩散方程; 交替方向隐格式; 收敛性; 稳定性 |
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二维半线性反应扩散方程的交替方向隐格式
吴宏伟
东南大学数学系, 南京, 210096
本文研究一类二维半线性反应扩散方程的差分方法. 构造了一个二层线性化交替方向隐格式. 利用离散能量估计方法证明了差分格式解的存在唯一性、差分格式在离散$H^1$模下的二阶收敛性和稳定性.最后给出两个数值例子验证了理论分析结果.
AN ALTERNATING DIRECTION IMPLICIT DIFFERENCE SCHEME FOR TWO DIMENSIONAL SEMILINEAR REACTION-DIFFUSION EQUATION
Wu Hongwei
Department of Mathematics, Southeast University, Nanjing 210096, China
The purpose of this work is to study difference method for a two dimensional semilinear 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.
国家自然科学基金(10471023)和江苏省自然科学基金(BK2007101) 资助项目.