Numerical solution of the static beam problem by Bernoulli collocation method

Quanwei Ren; Hongjiong Tian

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Numerical solution of the static beam problem by Bernoulli collocation method

机译：伯努利搭配法数值求解静力梁问题

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摘要

We propose a numerical scheme to obtain an approximate solution of a boundary value problem for fourth order nonlinear integro-differential equation of Kirchhoff type. We first reduce the problem to a nonlinear finite dimensional system based on the Bernoulli polynomial approximation and then solve it by an iterative process together with a collocation method. Convergence of the iterative process and error estimates of the approximate solution are provided. Numerical experiments are conducted to illustrate the performance of the proposed method.

机译：我们提出了一个数值方案，以获得基尔霍夫型四阶非线性积分微分方程的边值问题的近似解。我们首先将问题简化为基于伯努利多项式逼近的非线性有限维系统，然后通过迭代过程和搭配方法对其进行求解。提供了迭代过程的收敛性和近似解决方案的误差估计。数值实验表明了该方法的性能。

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来源
《Applied Mathematical Modelling》 |2016年第22期|8886-8897|共12页
作者
Quanwei Ren; Hongjiong Tian;
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作者单位

Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, PR China;

Department of Mathematics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, PR China,Department of Mathematics, Shanghai Normal University, Division of Computational Science, E-Institute of Shanghai Universities, Scientific Computing Key Laboratory of Shanghai Universities, 100 Guilin Road, Shanghai 200234, PR China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Bernoulli polynomial; Collocation method; Nonlinear fourth order integro-differential; equation; Iterative process; Error estimate;

机译：伯努利多项式;搭配方法;非线性四阶积分微分;方程;迭代过程;误差估计;

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Numerical solution of the static beam problem by Bernoulli collocation method

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