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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (1): 43-55.doi: 10.3969/j.issn.1005-3085.2020.01.004

• • 上一篇    下一篇

长短波方程的两个守恒型紧致有限差分格式

蒋佳平,  王廷春   

  1. 南京信息工程大学数学与统计学院，南京 210044
  • 收稿日期:2017-09-06 接受日期:2018-01-15 出版日期:2020-02-15 发布日期:2020-04-15
  • 基金资助:
    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.

Two Conservative Compact Finite Difference Schemes for the Long-wave Short-wave Interaction Equation

JIANG Jia-ping,  WANG Ting-chun   

  1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044
  • Received:2017-09-06 Accepted:2018-01-15 Online:2020-02-15 Published:2020-04-15
  • Supported by:
    The National Natural Science Foundation of China (11571181); the Natural Science Foundation of Jiangsu Province (BK20171454); Jiangsu Qinglan Project.

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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．

关键词: 长短波方程, 紧致有限差分格式, 质量守恒, 能量守恒

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.

Key words: long-wave short-wave interaction equation, compact finite difference scheme, mass conservation law, energy conservation law

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