期刊文献+

一类四阶微积分方程的紧差分格式 预览

Compact Difference for a Class of Fourth-Order Integro-Differential Equations
在线阅读 下载PDF
收藏 分享 导出
摘要 针对由铰链梁横向振动模型而建立的四阶微积分方程,提出紧差分格式进行求解,利用Newton型迭代法处理积分项,给出差分格式解的存在性、收敛性和稳定性的证明.数值结果表明:格式的精度为O(ht). A compact difference scheme is proposed to solve the fourth-order integro-differential equation arising from the transverse vibrations of the hinge model. Newton type iteration methods are presented to deal with the integral term. The existence, convergence and stability of the scheme are also proved. Numerical results show that the accuracy order of the Scheme is of O(h4 ).
作者 任全伟 庄清渠 REN Quan-wei, ZHUANG Qing-qu (School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China)
出处 《华侨大学学报:自然科学版》 CAS 北大核心 2014年第2期232-237,共6页 Journal of Huaqiao University(Natural Science)
基金 国家自然科学基金资助项目(11126330) 福建省自然科学基金资助项目(20liJ05005)
关键词 四阶微积分方程 紧差分格式 迭代算法 收敛性 稳定性 Keywords: fourth-order integro-differential equation compact difference scheme iterative algorithm convergence sta-bility
  • 相关文献

参考文献11

  • 1FEIREISL E.Exponential attractors for non-autonomous systems: Long-time behaviour of vibrating beams[J].Mathematical Methods in the Applied Sciences,1992,15(4):287-297. 被引量:1
  • 2SHIN J Y.Finite-element approximation of a fourth-order differential equation[J].Computers and Mathematics with Applications,1998,35(8):95-100. 被引量:1
  • 3OHM M R,LEE H Y,SHIN J Y.Error estimates of finite-element approximations for a fourth-order differential equation[J].Computers and Mathematics with Applications,2006,52(3/4):283-288. 被引量:1
  • 4DANG Q A,LUAN V T.Iterative method for solving a nonlinear fourth order boundary value problem[J].Computers and Mathematics with Applications,2010,60(1):112-121. 被引量:1
  • 5SEMPER B.Finite element methods for suspension bridge models[J].Computers and Mathematics with Applications,1993,26(5):77-91. 被引量:1
  • 6庄清渠,任全伟.一类四阶微积分方程的差分迭代解法[J].华侨大学学报:自然科学版,2012,33(6):709-714. 被引量:3
  • 7孙志忠.偏微分方程数值解法[M].北京:科学出版社,2012:13-15. 被引量:2
  • 8SHIDAMA Y.The Taylor expansions[J].Formalized Mathematics,2004,12(2):195-200. 被引量:1
  • 9SHERMAN A H.On Newton-iterative methods for the solution of systems of nonlinear equations[J].SIAM Journal on Numerical Analysis,1978,15(4):755-771. 被引量:1
  • 10DAVIS P J,RABINOWITZ P.Methods of numerical integration[M].New York: Dover Publications,2007:57-60. 被引量:1

二级参考文献12

  • 1DANG Q A, LET S. Iterative method for solving a problem with mixed boundary conditions for biharmonic equation [J]. Adv Appl Math Mech, 2009,1(5) : 683-698. 被引量:1
  • 2DANG Q A, LUAN V T. Iterative method for solving a nonlinear fourth order boundary value problem[J]. Computers and Mathematics with Applieations, 2010,60(1):112-121. 被引量:1
  • 3ZHUANG Qing-qu. A Legendre spectral-element method for the one-dimensional fourth-order equations[J]. Applied Mathematics and Computation, 2011,218(7) : 3587-3595. 被引量:1
  • 4KARMAN T, BlOT M A. Mathematical methods in engineering[M]. New York: McGraw-Hill, 1940. 被引量:1
  • 5SEMPER B. Finite element methods for suspension bridge models[J]. Computers and Mathematics with Applica- tions, 1993,26(5) : 77-91. 被引量:1
  • 6SEMPER B. Finite element approximation of a fourth order integro-differential equation[J]. Applied Mathematics Letters, 1994,7 (1) : 59-62. 被引量:1
  • 7BREZZI F, FORTIN M. Mixed and hybrid finite element methods[M]. New York:Springer-Verlag, 1991. 被引量:1
  • 8SHERMAN A H. On newton-iterative methods for the solution of systems of nonlinear equations[J]. SIAM Journal on Numerical Analysis, 1978,15(4) :755-771. 被引量:1
  • 9KUSRAEV A G. Discrete maximum principle[J]. Mathematical Notes, 1983,34(2) :617-620. 被引量:1
  • 10FEIREISI E. Exponential attractors for non-autonomous systems: Long-time behaviour of vibrating beams[J]. Mathematical methods in the applied sciences, 1992,15(4):287-297. 被引量:1

共引文献3

投稿分析
职称考试

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 意见反馈