东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2013, Vol. 34 ›› Issue (5): 757-760.DOI: -

• 数学 • 上一篇    

广义RosenauBurgers方程的一个差分格式

邵新慧，薛冠宇，张铁   

  1. (东北大学理学院，辽宁沈阳110819)
  • 收稿日期:2012-05-28 修回日期:2012-05-28 出版日期:2013-05-15 发布日期:2013-07-09
  • 通讯作者: 邵新慧
  • 作者简介:邵新慧(1970-)，女，山东青岛人，东北大学副教授.
  • 基金资助:
    国家自然科学基金资助项目(11071033)；中央高校基本科研业务费专项资金资助项目(090405013).

A Finite Difference Scheme for Generalized RosenauBurgers Equation〓

SHAO Xinhui， XUE Guanyu， ZHANG Tie   

  1. School of Sciences， Northeastern University， Shenyang 110819， China.
  • Received:2012-05-28 Revised:2012-05-28 Online:2013-05-15 Published:2013-07-09
  • Contact: SHAO Xinhui
  • About author:-
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摘要： 从动力学系统的实际问题出发，对广义RosenauBurgers方程的初边值问题进行了数值研究，揭示了复杂离散动态系统理论中非线性波耗散问题.提出了一个新的两层隐式差分格式，对差分解进行了先验估计，得到了差分解的存在唯一性，并给出了该差分格式的收敛性和稳定性的严格理论.数值实验结果表明该方法简单而有效、稳定性良好.该格式具有理论意义和推广价值.

关键词: 广义RosenauBurgers方程, 有限差分格式, 可解性, 收敛性, 稳定性

Abstract: Based on the study of the dynamic systems， the numerical method of the initialboundary value problem of generalized RosenauBurgers equation was discussed and the dissipation problems of nonlinear wave were revealed. A new implicit finite difference scheme of twolevel was proposed and the prior estimate of the finite difference solution was obtained. Existence and uniqueness of numerical solutions were derived. It was proved that the finite difference scheme is convergent and stable. Numerical experiments indicated the scheme is efficient and good stability， the proposed scheme has theoretical significance and availability.

Key words: generalized RosenauBurgers equation, finite difference scheme, solvability, convergence, stability

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