全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

一类四阶微积分方程的紧差分格式

DOI: 10.11830/ISSN.1000-5013.2014.02.0232

Keywords: 四阶微积分方程, 紧差分格式, 迭代算法, 收敛性, 稳定性

Full-Text   Cite this paper   Add to My Lib

Abstract:

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(h4).

References

[1]  FEIREISL 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.
[2]  SHIN J Y.Finite-element approximation of a fourth-order differential equation[J].Computers and Mathematics with Applications,1998,35(8):95-100.
[3]  OHM 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.
[4]  DANG 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.
[5]  SEMPER B.Finite element methods for suspension bridge models[J].Computers and Mathematics with Applications,1993,26(5):77-91.
[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.
[7]  孙志忠.偏微分方程数值解法[M].北京:科学出版社,2012:13-15.
[8]  SHIDAMA Y.The Taylor expansions[J].Formalized Mathematics,2004,12(2):195-200.
[9]  SHERMAN 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.
[10]  DAVIS P J,RABINOWITZ P.Methods of numerical integration[M].New York: Dover Publications,2007:57-60.
[11]  GAUTSCHI W.Numerical analysis[M].Berlin: Birkhauser Boston,2011:168-178.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133