| 变系数反应扩散方程的差分解法 |
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| 引用本文： | 罗卫华,邬凌,王彬.变系数反应扩散方程的差分解法[J].西南师范大学学报(自然科学版),2011,36(4). |
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| 作者姓名： | 罗卫华 邬凌 王彬 |
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| 作者单位： | 内江师范学院四川省高等学校数值仿真重点实验室,四川内江,641112 |
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| 基金项目： | 四川省教育厅重点实验室项目，内江师范学院青年基金项目 |
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| 摘 要： | 研究了变系数反应扩散方程的差分格式.首先用Taylor公式导出紧差分格式；再通过补充边界值给出了此格式的求解形式；接着用能量方法证明了差分格式的解的存在性、唯一性、稳定性和收敛性；最后用数值例子验证了此方法的可行性和精确度.
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| 关 键 词： | 反应扩散方程 差分格式 变系数 |
A Compact Difference Method for the Variable Coefficient Reaction Diffusion Equations |
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| LUO Wei-hua,WU Ling,WANG Bin.A Compact Difference Method for the Variable Coefficient Reaction Diffusion Equations[J].Journal of Southwest China Normal University(Natural Science),2011,36(4). |
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| Authors: | LUO Wei-hua WU Ling WANG Bin |
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| Institution: | LUO Wei-hua,WU Ling,WANG BinKey Laboratory of Numerical Simulation of Sichuan Province,Neijiang Normal University,Neijiang Sichuan 641112,China |
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| Abstract: | A difference method for a variable coefficient reaction diffusion equation is studied.Firstly,a compact difference method is established using the Taylor formula.Secondly,by supplementing boundary values,the system of linear equations corresponding to the difference method becomes solved.Thirdly,by using the energy analysis method,the existence and uniqueness,the stability and convergence are all proved.Lastly,an example is given to show the feasibility and accuracy of the difference scheme. |
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| Keywords: | reaction diffusion equation finite difference variable coefficient |
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