| 广义sine-Gordon方程高精度隐式紧致差分方法 |
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| 引用本文： | 耿晓月,刘小华.广义sine-Gordon方程高精度隐式紧致差分方法[J].计算数学,2015,37(2):199-212. |
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| 作者姓名： | 耿晓月 刘小华 |
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| 作者单位： | 西南石油大学理学院, 成都 637001 |
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| 摘 要： | 本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度.
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| 关 键 词： | SG方程 紧致差分格式 交替方向隐格式 外推法 能量分析法 |
| 收稿时间： | 2014-09-18; |
A HIGH ACCURACY IMPLICIT COMPACT DIFFERENCE METHOD FOR SOLVING THE GENERALIZED SINE-GORDON EQUATION |
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| Geng Xiaoyue,Liu Xiaohua.A HIGH ACCURACY IMPLICIT COMPACT DIFFERENCE METHOD FOR SOLVING THE GENERALIZED SINE-GORDON EQUATION[J].Mathematica Numerica Sinica,2015,37(2):199-212. |
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| Authors: | Geng Xiaoyue Liu Xiaohua |
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| Institution: | College of Science, Southwest Petroleum University, Chengdu 637001, China |
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| Abstract: | For solving two-dimensional nonlinear generalized sine-Gordon(SG) equations, we established a three-level high order compact alternating direction implicit scheme. Applying the energy analysis method, we obtain that the scheme is convergent to be fourth-order spatial accuracy and second-order temporal accuracy. An implemental Richardson extrapolation method is developed to improve temporal accuracy. The numerical results are provided to verify the algorithm has ability to reach fourth-order accuracy in both time and space. |
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| Keywords: | SG equations Compact finite difference scheme alternating direction implicit schemes extrapolation method energy method |
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