| 对流扩散方程的半拉格朗日有限差分法 |
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| 引用本文： | 邵光茹,龙晓瀚.对流扩散方程的半拉格朗日有限差分法[J].鲁东大学学报,2014(2):114-120. |
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| 作者姓名： | 邵光茹 龙晓瀚 |
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| 作者单位： | [1]大连理工大学数学科学学院,辽宁大连116023 [2]鲁东大学数学与统计科学学院,山东烟台264039 |
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| 基金项目： | 山东省自然科学基金的资助项目（ZR2010AL021） |
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| 摘 要： | 针对二维对流扩散方程提出了半拉格朗日Crank-Nicolson有限差分格式.化对流扩散方程成拉格朗日形式,然后进行时间和空间离散.时间的离散采用Crank-Nicolson格式,空间离散采用有限差分格式.数值实验表明,新建格式是稳定和收敛的.
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| 关 键 词： | 对流扩散方程 半拉格朗日法 Crank-Nicolson格式 有限差分法 |
Semi-Lagrangian Finite Difference Methods for Convection-diffusion Equations |
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| SHAO Guang-ru,LONG Xiao-han.Semi-Lagrangian Finite Difference Methods for Convection-diffusion Equations[J].Ludong University Journal (Natural Science Edition),2014(2):114-120. |
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| Authors: | SHAO Guang-ru LONG Xiao-han |
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| Institution: | 1. School of Mathematic Science, Dalian University of Technology, Dalian 116023, China; 2. School of Mathematics and Statistics Science, Ludong University, Yantai 264039 ,China) |
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| Abstract: | Semi-Lagrangian Crank-Nicolson method for two-dimension convection-diffusion equations is presented. First,convection-diffusion equation is transformed into the Lagrangian form. Second,time and space variables are discretized,respectively. Crank-Nicolson method is used for time discretization and finite difference method for space discretization. Numerical experiments show that the numerical method built in this paper is efficient,stable and convergent. |
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| Keywords: | convection-diffusion equation semi-Lagrangian method Crank-Nicolson scheme finite difference method |
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