数学物理学报

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对称正则长波方程的拟紧致守恒差分逼近

王廷春; 张鲁明   

  1. 南京航空航天大学航空宇航学院, 南京 210016
  • 收稿日期:2005-12-12 修回日期:2006-05-31 出版日期:2006-12-25 发布日期:2006-12-25
  • 通讯作者: 王廷春
  • 基金资助:
    国家自然科学基金(10572057, 10471023)资助

Pseudo-Compact Conservative Finite Difference Approximate Solution for the Symmetric Regularized-Long-Wave Equation

Wang Tingchun; Zhang Luming   

  1. Nanjing University of Aeronautics and Astronautics, College of Aerospace Engineering, Nanjing 210016
  • Received:2005-12-12 Revised:2006-05-31 Online:2006-12-25 Published:2006-12-25
  • Contact: Wang Tingchun

摘要: 该文对称正则长波方程的初边值问题进行了数值研究, 提出了一个两层隐式拟紧差分格式,格式很好地模拟了初值问题的守恒性质. 得到了差分解的存在唯一性, 并在先验估计基础上运用能量方法分析了格式的稳定性及二阶收敛性.

关键词: 对称正则长波方程, 差分格式, 守恒, 收敛性

Abstract: In this paper, a pseudo-compact finite difference scheme is proposed for symmetric Regularized-Long-wave(SRLW) equation. Existence and uniquence of numerical solutions are shown. A priori estimate and second order convergence as well as conservation of energy of the finite difference approxmate solution are discussed.

Key words: SRLW Equation, Difference scheme, Conservation, Convergence

中图分类号: 

  • 65M06