| 求解广义improved KdV方程的守恒差分算法 |
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| 引用本文： | 郑茂波,谭宁波. 求解广义improved KdV方程的守恒差分算法[J]. 四川大学学报(自然科学版), 2017, 54(4): 688-692 |
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| 作者姓名： | 郑茂波 谭宁波 |
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| 作者单位： | 成都工业学院,成都工业学院 |
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| 摘 要： | 本文对广义improved KdV方程的初边值问题进行了数值研究，提出了一个两层非线性有限差分格式，该格式合理地模拟了方程本身具有的两个守恒律。讨论了差分解的存在唯一性，并在其差分解的先验估计的基础上利用能量方法分析了该格式的二阶收敛性与无条件稳定性，数值算例表明本文的格式是可行的。
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| 关 键 词： | 广义improved KdV方程 差分格式 守恒性；收敛性 稳定性 |
| 收稿时间： | 2016-08-31 |
| 修稿时间： | 2017-03-21 |
Conservative Difference Scheme for the General improved KdV Equation |
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| ZHENG Mao-Bo and TAN Ning-Bo. Conservative Difference Scheme for the General improved KdV Equation[J]. Journal of Sichuan University (Natural Science Edition), 2017, 54(4): 688-692 |
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| Authors: | ZHENG Mao-Bo and TAN Ning-Bo |
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| Affiliation: | Chengdu Technological University and Chengdu Technological University |
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| Abstract: | In this paper, a conservative difference scheme for an initial-boundary value problem of the general improved KdV equation is proposed. This scheme simulates the two conservation properties of the problem well. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, second order convergence and unconditional stability are discussed.Numerical examples show the availability of scheme. |
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| Keywords: | the general improved KdV equation finite difference scheme conservation properties convergence stability |
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