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一类四阶微积分方程的差分迭代解法 被引量：3

Finite Difference Approximation of a Class of Fourth-Order Integro-Differential Equations
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摘要 针对研究吊桥模型而建立的四阶微积分方程,提出利用有限差分法进行求解.采用Newton型迭代法处理非线性项,大大提高了收敛效率,并给出差分逼近的误差分析.数值算例说明了算法的可行性和有效性. Finite difference method is proposed to approximate a fourth-order integro-differential equation modeling the suspension bridge.Newton type iteration methods are used to deal with the nonlinear term,which greatly improve the computational efficiency.Moreover,error estimate of the finite difference approximation is obtained.Numerical experiments are given to confirm the feasibility and efficiency of the algorithm.
作者 庄清渠 任全伟
机构地区 华侨大学数学科学学院
出处 《华侨大学学报（自然科学版）》 CAS 北大核心 2012年第6期709-714,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(2011J05005) 中央高校基本科研业务费专项基金资助项目 国务院侨办科研基金资助项目(10QZR21)
关键词 四阶微积分方程 差分方法 迭代算法 误差分析 fourth-order integro-differential equation finite-difference method iterative algorithm error estimate
分类号 O241.8 [理学—计算数学]
  • 相关文献

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.
  • 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.
  • 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.
  • 4KARMAN T, BlOT M A. Mathematical methods in engineering[M]. New York: McGraw-Hill, 1940.
  • 5SEMPER B. Finite element methods for suspension bridge models[J]. Computers and Mathematics with Applica- tions, 1993,26(5) : 77-91.
  • 6SEMPER B. Finite element approximation of a fourth order integro-differential equation[J]. Applied Mathematics Letters, 1994,7 (1) : 59-62.
  • 7BREZZI F, FORTIN M. Mixed and hybrid finite element methods[M]. New York:Springer-Verlag, 1991.
  • 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.
  • 9KUSRAEV A G. Discrete maximum principle[J]. Mathematical Notes, 1983,34(2) :617-620.
  • 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.

同被引文献20

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

引证文献3

二级引证文献3

华侨大学学报（自然科学版）
2012年 第6期

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