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求解广义Rosenau-Kawahara方程的一个守恒差分格式 被引量：3

A conservation difference scheme for generalized Rosenau-Kawahara equation
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摘要 对一类广义Rosenau-Kawahara方程的初边值问题进行数值研究,提出了一个两层非线性有限差分格式,合理模拟了问题的两个守恒性质,得到了差分解的先验估计和存在唯一性;利用能量方法分析了差分格式的二阶收敛性与无条件稳定性;最后,利用数值算例验证了差分格式的有效性. The numerical solution of the initial‐boundary value problem for generalized Rosenau‐Kawahara equation is considered , and a nonlinear two‐level finite difference scheme is designed . The difference schemes simulate two conservative quantities of the problem well . The prior estimate , existence and uniqueness of the finite difference solution are also obtained . It is show n that the finite difference scheme is second‐order convergence and unconditionally stable by discrete functional analysis method . Numerical experiments verify the theoretical results .
作者 陈涛 胡劲松
机构地区 西华大学数学与计算机学院
出处 《西北师范大学学报（自然科学版）》 CAS 北大核心 2015年第5期18-21,26,共5页 Journal of Northwest Normal University(Natural Science)
基金 国家自然科学基金资助项目(11171239) 西华大学研究生创新基金资助课题(ycjj2014033)
关键词 广义Rosenau-Kawahara方程 有限差分格式 守恒性 收敛性 稳定性 generalized Rosenau-Kaw ahara equation finite difference scheme conservation convergence stability
分类号 O241.82 [理学—计算数学]
  • 相关文献

参考文献10

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二级参考文献20

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共引文献13

同被引文献23

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  • 3ZUO J M. Solitons and periodic solutions for the Rosenau-KdV and Rosenau-Kawahara equations [ J ]. Applied Mathematics and Computation,2009,215 ( 2 ) : 835 - 840.
  • 4BISWAS A, TRIKI H, LABIDI M. Bright and dark solitons of the Rosenau-Kawahara equation with power law nonlinearity [ J ]. Physics of Wave Phenomena,2011,19 ( 1 ) :24 - 29.
  • 5HU J, XU Y, HU B, et al. Two conservative difference schemes for Rosenau-Kawahara equation. Advances in Mathematical Physics, 2014,10( 1 ) :396 - 409.
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  • 10Cui yanfen, Mao De - kang. Numerical Method Satisfying the First Two Conservation Laws for the Korteweg - de Vries Equation [Journal of Computational Physics ,2 0 0 7 ,227( 1) : 376.

引证文献3

二级引证文献1

西北师范大学学报（自然科学版）
2015年 第5期

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