| 长短波方程的两个守恒型紧致有限差分格式 |
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| 引用本文： | 蒋佳平,王廷春.长短波方程的两个守恒型紧致有限差分格式[J].工程数学学报,2020,37(1):43-55. |
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| 作者姓名： | 蒋佳平 王廷春 |
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| 作者单位： | 南京信息工程大学数学与统计学院，南京210044 |
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| 基金项目： | 国家自然科学基金(11571181);江苏省自然科学基金(BK20171454);江苏省青蓝工程~~ |
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| 摘 要： | 本文对一类耦合非线性长短波方程组进行了数值研究，提出了两个四阶紧致有限差分格式，并证明新格式在离散意义下保持原问题的两个守恒性质，即总质量守恒和总能量守恒．数值实验表明本文格式在时间和空间方向分别具有二阶和四阶精度，具有良好的稳定性且在离散意义下很好地保持总质量和总能量守恒．
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| 关 键 词： | 长短波方程 紧致有限差分格式 质量守恒 能量守恒 |
| 收稿时间： | 2017-09-06 |
Two Conservative Compact Finite Difference Schemes for the Long-wave Short-wave Interaction Equation |
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| JIANG Jia-ping,WANG Ting-chun.Two Conservative Compact Finite Difference Schemes for the Long-wave Short-wave Interaction Equation[J].Chinese Journal of Engineering Mathematics,2020,37(1):43-55. |
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| Authors: | JIANG Jia-ping WANG Ting-chun |
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| Affiliation: | College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044 |
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| Abstract: | This paper focuses on numerical simulation of the long-wave short-wave interaction equation.Two fourth-order compact finite difference schemes are proposed and proved to preserve the total mass and energy in the discrete sense.Numerical results show the good stability of the schemes and fourth-order and second-order convergence of the numerical solutions in space and time,respectively.Simulation results also show that the schemes preserve well the total mass and energy. |
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| Keywords: | long-wave short-wave interaction equation compact finite difference scheme mass conservation law energy conservation law |
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