| 一种求解对流扩散反应方程的高阶紧致差分格式 |
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| 引用本文： | 杨录峰,李春光.一种求解对流扩散反应方程的高阶紧致差分格式[J].宁夏大学学报(自然科学版),2013(2):101-104,109. |
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| 作者姓名： | 杨录峰 李春光 |
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| 作者单位： | [1]北方民族大学信息与计算科学学院,宁夏银川750021 [2]北方民族大学数值计算与工程应用研究所,宁夏银川750021 |
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| 基金项目： | 国家自然科学基金资助项目（10961002）;北方民族大学自主科研项目（2011ZQY026） |
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| 摘 要： | 提出一种消除对流扩散反应方程中对流项的处理技巧,结合中心差分格式的新方法与相同节点的迎风差分格式相比具有更好的精度,该方法很容易与Padé格式相结合,构造出具有四阶精度的无条件稳定的高阶差分格式.数值实验表明,新方法具有很好的精度和健壮性,并且可以有效求解对流占优问题.
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| 关 键 词： | 紧致差分格式 无条件稳定 对流扩散反应方程 对流占优 |
A High-Order Compact Finite Difference Scheme for Solving the Convection Diffusion Reaction Equations |
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| Yang Lufeng,Li Chunguang.A High-Order Compact Finite Difference Scheme for Solving the Convection Diffusion Reaction Equations[J].Journal of Ningxia University(Natural Science Edition),2013(2):101-104,109. |
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| Authors: | Yang Lufeng Li Chunguang |
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| Institution: | 1. School of Information and Computation Science, Beifang University of Nationalities, Yinchuan 750021, China; 2. Research Institute of Numerical Computation and Engineering Application, Beifang University of Nationalities, Yinchuan 750021, China) |
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| Abstract: | A method to eliminate the convection term from convection diffusion reaction equations ;s presented in this paper. The new method, combined with the central difference schemes, can achieve better accuracy than the upwind schemes on the same finite difference stencil. It can also be easily combined with the Pad4 approximation to achieve fourth-order accuracy, and unconditional stability is also proved. Numerical examples involving one dimensional equations is presented in the paper to demonstrate the accuracy and robustness of the new approaches and they can effectively solve the convection dominate problems. |
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| Keywords: | compact difference scheme unconditional stability convection diffusion reaction equations convection dominate |
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