期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Bona-Smith方程的同伦分析方法研究 被引量：1

Solution of Bona-Smith Systems Using Homotopy Analysis Method
下载PDF
导出
摘要 应用同伦分析方法求解Bona-Smith方程.通过对同伦分析方法得到的解与精确解相比较,表明这种解析方法能够有效地处理该非线性问题,并且提供了一种简便的方式来控制收敛区域和级数解的收敛率. Bona-Smith systems are solved by an efficient technique named homotopy analysis method. The comparisons are made between the results of the homotopy analysis method and the exact solution. It indicates that homotopy analysis method is valid for dealing with the nonlinearity and provides a convenient way of controlling the convergence region and rate ＆the series solution.
作者 汤可 黄鹏展 马小玲
机构地区 新疆大学数学与系统科学学院
出处 《伊犁师范学院学报（自然科学版）》 2013年第3期19-24,共6页 Journal of Yili Normal University：Natural Science Edition
基金 新疆维吾尔自治区自然科学基金资助项目(2013211B01) 新疆大学博士启动基金资助项目(BS120102) 新疆大学校院联合资助项目(XY110102)
关键词 Bona-Smith方程 同伦分析方法 级数解 收敛性分析 Bona-Smith systems Homotopy analysis method Series solution Convergence analysis
分类号 O174 [理学—基础数学]
  • 相关文献

参考文献15

  • 1Bona J L, Smith R. A model for the two-way propagation of water waves in a channel [J]. Math. Proc. Camb. Philos. Soc., 1976, 79: 167-182.
  • 2Antonopoulos D C, Dougalis V A, Mitsotakis D E. Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems[J]. Adv. Differ. Equ., 2009, 14: 27-53.
  • 3Winther R. A finite element method for a version of the Boussinesq equations[J]. SIAMJ. Numer. Anal., 1982, 19: 561-570.
  • 4Pelloni B, Dougalis V A.. Numerical modelling of two-way propagation of nonlinear dispersive waves[J]. Math. Comput.Simul., 2001, 55: 595-606.
  • 5Antonopoulos D C, Dougalis V A, Mitsotakis D E. Numerical solution of Boussinesq systems of the Bona-Smith familyJ]. Appl. Numer. Math., 2010, 60: 314-336.
  • 6Liao S J. The proposed homotopy analysis technique for the solution of nonlinear problemsEC]. Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
  • 7Eynde R V. Historical evolution of the concept homotopic paths[J]. Arch. Hist. Exact. Sci., 1992, 45: 128-188.
  • 8Liao S J. A kind of approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics[J]. Int. J. Nonlinear Mech., 1997, 32: 815-822.
  • 9Liao S J. An explicit, totally analytic approximation of Blasius' viscous flow problems [J]. Int. J. Nonlinear Mech., 1999, 34: 759-778.
  • 10Liao S J, Cheung K F. Homotopy analysis of nonlinear progressive waves in deep Water[J]. J. Eng. Math., 2003, 45: 105-116.

同被引文献7

  • 1Liao S J. The proposed homotopy analysis technique for the solution of nonlinear problems [D]. Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
  • 2田金燕.两种改进的同伦分析方法[D].哈尔滨理工大学硕士学位论文,2012.
  • 3Liao S J. Notes on the homotopy analysis method: some definitions and theorems [ J ]. Commun. Nonlinear Sci. Numer. Simul, 2009, 14: 983-997.
  • 4Inc M. On numerical solution of Burgers' equation by homotopy analysis method [J ]. Phys. Lett. A, 2008, 372: 356-360.
  • 5He J H. Homotopy perturbation technique[J]. Comput. Meth. Appl. Mech. Eng. , 1999, 178: 257-262.
  • 6Liao S J. Beyond Perturbation: Introduction to the Homotopy Analysis Method [ M ]. Chapman & Hall/CRC, Boca Raton, 2003.
  • 7韩元春,那仁满都拉.改进同伦分析方法及非线性热传导问题的同伦解[J].四川师范大学学报（自然科学版）,2014,37(3):375-379. 被引量：4

引证文献1

二级引证文献2

伊犁师范学院学报（自然科学版）
2013年 第3期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部