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A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation

机译：基于伯努利运算矩阵的配置方法求解非线性BVP，该非线性BVP是由微分学问题引起的

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摘要

A new collocation method is developed for solving BVPs which arise from the problems in calculus of variation. These BVPs result from the Euler-Lagrange equations, which are the necessary conditions of the extremums of problems in calculus of variation. The proposed method is based upon the Bernoulli polynomials approximation together with their operational matrix of differentiation. After imposing the collocation nodes to the main BVPs, we reduce the variational problems to the solution of algebraic equations. It should be noted that the robustness of operational matrices of differentiation with respect to the integration ones is shown through illustrative examples. Complete comparisons with other methods and superior results confirm the validity and applicability of the presented method.
机译：开发了一种新的搭配方法来解决BVPs，它是由变异演算中的问题引起的。这些BVP由Euler-Lagrange方程得出，Euler-Lagrange方程是变异演算中问题极值的必要条件。所提出的方法基于伯努利多项式逼近以及它们的微分运算矩阵。将搭配节点强加给主要的BVP后，我们将变分问题减少到代数方程的解。应当注意，通过说明性示例示出了关于积分运算的微分运算矩阵的鲁棒性。与其他方法的完全比较和优异的结果证实了所提出方法的有效性和适用性。

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  • 来源
    《Mathematical Problems in Engineering》 |2013年第3期|757206.1-757206.9|共9页
  • 作者

    Emran Tohidi; Adem Kilicman;

  • 作者单位

    Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran;

    Department of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia;

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