| 二维半线性反应扩散方程的交替方向隐格式 |
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| 引用本文： | 吴宏伟.二维半线性反应扩散方程的交替方向隐格式[J].计算数学,2008,30(4):349-360. |
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| 作者姓名： | 吴宏伟 |
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| 作者单位： | 东南大学数学系,南京,210096 |
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| 基金项目： | 国家自然科学基金
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江苏省自然科学基金
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| 摘 要： | 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.
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| 关 键 词： | 半线性 反应扩散方程 交替方向隐格式 收敛性 稳定性 |
AN ALTERNATING DIRECTION IMPLICIT DIFFERENCE SCHEME FOR TWO DIMENSIONAL SEMILINEAR REACTION-DIFFUSION EQUATION |
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| Wu Hongwei.AN ALTERNATING DIRECTION IMPLICIT DIFFERENCE SCHEME FOR TWO DIMENSIONAL SEMILINEAR REACTION-DIFFUSION EQUATION[J].Mathematica Numerica Sinica,2008,30(4):349-360. |
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| Authors: | Wu Hongwei |
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| Institution: | Department of Mathematics, Southeast University, Nanjing 210096, China |
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| Abstract: | 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. |
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| Keywords: | semilinear reaction-diffusion equation ADI difference scheme convergence stability |
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