| 基于Hopf-Cole变换的二维Burgers方程的新数值解法 |
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| 引用本文： | 贾彦娜,张艳波,阿布都外力.基于Hopf-Cole变换的二维Burgers方程的新数值解法[J].山西师范大学学报,2012(3):11-16. |
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| 作者姓名： | 贾彦娜 张艳波 阿布都外力 |
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| 作者单位： | 山东现代职业学院;新疆大学数学与系统科学学院 |
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| 基金项目： | 国家自然科学基金(10961024);新疆高校科研计划资助(XJEDU2007I02) |
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| 摘 要： | 讨论了二维Burgers方程初边值问题的数值解法.新的方法是基于二维Hopf-Cole变换,将Bur-gers方程的初边值问题相应的变为热传导方程的初边值问题,用修正局部Crank-Nicolson法进行求解,得到了较好的结果,然后再进行逆变换得出原Burgers方程的解.同时也给出了稳定性、相容性及收敛性的理论证明.数值实验结果表明了该方法的正确性和格式的有效性。
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| 关 键 词： | Burgers方程 Hopf-Cole变换 修正局部Crank-Nicolson法 收敛性 稳定性 |
A New Numerical Method Based on Hopf-cole Transformation for Two Dimensional Burgers Equation |
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| Institution: | JIA Yan-na1,ZHANG Yan-bo1,Abduwali2*(1.Shandong Modern Vocational College,Jinan 250104,Shandong,China;2.College of Mathematics and Systems Science,Xinjiang University,Urumchi 830000,Xinjiang,China) |
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| Abstract: | In this paper,we discuss a numerical method of two dimensional Burgers equation for the initial-boundary value problem.Based on the two-dimensional Hopf-Cole transformation,the new method transforms initial-boundary value problem of Burgers equation to initial-boundary value problem of heat equation by using Hopf-Cole transformation.We use Modified Local Crank-Nicolson Method for heat equation,and obtain a better solution for Burgers equation in inverse transform method.And we give a corresponding theoretical proof for stability,consistence and convergence.The numerical experiment shows the theoretical accuracy and computational effectiveness of proposed method. |
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| Keywords: | Burgers equation Hopf-Cole transformation the Modified Local Crank-Nicolson Method stability convergence |
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