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

一类四阶微积分方程的Legendre-Galerkin谱逼近 被引量：2

LEGENDRE-GALERKIN SPECTRAL APPROXIMATION OF A CLASS OF FOURTH-ORDER INTEGRO-DIFFERENTIAL EQUATIONS
原文传递
导出
摘要 针对研究吊桥模型而建立的四阶微积分方程,提出Legendre谱逼近法进行求解.构造迭代算法来求解得到的线性系统,证明了迭代格式的收敛性,对问题进行了误差分析.数值算例验证了迭代的收敛性和方法的高精度. Legendre-Galerkin spectral approximation is proposed to solve the fourth-order integro- differential equation modeling the span suspension bridge. An iteration method is presented to solve the resulting linear system, the convergence of the iteration is proved. Error estima- tion of the method is also given. Numerical experiments are given to confirm the convergence of the iteration and high-accuracy of the method.
作者 任全伟 庄清渠
机构地区 华侨大学数学科学学院
出处 《计算数学》 CSCD 北大核心 2013年第2期125-136,共12页 Mathematica Numerica Sinica
基金 国家自然科学基金项目(No.11126330) 福建省自然科学基金项目(No.2011J05005) 中央高校基本科研业务费专项资金 华侨大学侨办科研基金资助项目(10QZR21)
关键词 四阶微积分方程 Legendre谱逼近 迭代算法 误差分析 Fourth-order integro-differential equation Legendre spectral approxima-tion Iterative method Error estimate
分类号 O241.82 [理学—计算数学]
  • 相关文献

参考文献15

  • 1Gottlieb D and Orszag S A. Numerical analysis of spectral methods[M]. SIAM, 1983.
  • 2Canuto C, Hussaini M Y, Quarteroni A and Zang T A. Spectral methods[M]. Springer, 2006.
  • 3Streett C L and Macaraeg M G. Spectral multi-domain for large-scale fluid dynamic simulations[J]. Applied Numerical Mathematics, 1989, 6(1-2): 123-139.
  • 4McCrory R L and Orszag S A. Spectral methods for multi-dimensional diffusion problems[J]. Journal of Computational Physics, 1980, 37(1): 93-112.
  • 5Jiang Y J. On spectral methods for volterra-type integro-differential equations[J]. Journal of computational and applied mathematics, 2009, 230(2): 333-340.
  • 6Yalginbas S, Sezer M and Sorkun H H. Legendre polynomial solutions of high-order linear fredholm integro-differential equations[J]. Applied Mathematics and Computation, 2009, 210(2): 334-349.
  • 7Krmn T and Blot M A. Mathematical methods in engineering, volume 8. McGraw-Hill New York, 1940.
  • 8Semper B. Finite element approximation of a fourth order integro-differential equation[J]. Applied Mathematics Letters, 1994, 7(1): 59-62.
  • 9Brezzi F(Franco) and Fortin M. Mixed and hybrid finite element methods[M]. Springer-Verlag, 1991.
  • 10Semper B. Finite element methods for suspension bridge models[J]. Computers and Mathematics with Applications, 1993, 26(5): 77-91.

同被引文献16

  • 1Xuhong Yu,Yunge Zhao,Zhongqing Wang.A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line[J].Journal of Mathematical Study,2018,51(2):196-213. 被引量：3
  • 2Karman T and Biot M A. Mathematical methods in engineering[M]. volume 8. McGraw-Hill New York,1940.
  • 3Brezzi F (Franco) and Fortin M. Mixed and hybrid finite element methods[M]. Springer-Verlag, 1991.
  • 4Semper B. Finite element methods for suspension bridge models[J]. Computers and Mathematics with Applications, 1993, 26(5): 77-9l.
  • 5Semper B. Finite element approximation of a fourth order integra-differential equation[J]. Applied Mathematics Letters, 1994, 7(1): 59-62.
  • 6Shidama Y. The taylor expansions[J]. Formalized Mathematics, 2004, 12(2): 195-200.
  • 7孙志忠.偏微分方程数值解法[M].科学出版社,2012.
  • 8Kusraev A G. Discrete maximum principle[J]. Mathematical Notes, 1983, 34(2): 617-620.
  • 9Sherman A H. On newton-iterative methods for the solution of systems of nonlinear equations[J]. SIAMJournal on Numerical Analysis, 1978, 15: 755-771.
  • 10Davis PJ and Rabinowitz P. Methods of numerical integration[M]. Dover Publications, 2007.

引证文献2

二级引证文献2

计算数学
2013年 第2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