标题： 一种求解梁方程的高效数值方法 显示英文标题

标题： An Efficient Numerical Method for an Approximate Solution of the Beam Equation

摘要： 本文提出了一种求解非定常欧拉-伯努利梁方程的水平型线方法数值格式。该问题最初被重新表述为一个一阶初值问题系统，并使用适当的单步差分格式来处理最高阶时间导数，从而得到一组稳态梁方程。然后通过三次Hermite插值基函数的有限元法迭代求解所得的稳态问题族。此迭代过程可获得非定常问题解及其导数的近似值。所有这些近似值均与精确解进行比较，以展示所提方法的性能。此外，通过对数刻度图讨论了稳态和非定常问题网格参数的优化。 显示英文摘要

摘要： In this paper, we propose a horizontal type method of lines numerical scheme for the unsteady Euler-Bernoulli beam equation. The problem is initially reformulated as a first order system of initial value problems and a suitable one-step difference scheme is used for the highest order temporal derivative which leads to a system of steady beam equations. Then resulted family of steady problems is solved iteratively by the finite element method with Hermite cubic basis functions. This iterative procedure leads to approximations for both the solution of the unsteady problem and its derivatives. All these approximations are compared with the exact ones to illustrate the performance of the proposed method. Moreover, the optimization of the mesh parameters is discussed for both steady and unsteady problems by logarithmic scale plot.