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首页> 外文期刊>Mathematical Problems in Engineering >Numerical and Analytical Study for Fourth-Order Integro-Differential Equations Using a Pseudospectral Method
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Numerical and Analytical Study for Fourth-Order Integro-Differential Equations Using a Pseudospectral Method

机译：用伪谱方法对四阶积分微分方程进行数值和解析研究

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摘要

A numerical method for solving fourth-order integro-differential equations is presented. This method is based on replacement of the unknown function by a truncated series of well-known shifted Chebyshev expansion of functions. An approximate formula of the integer derivative is introduced. The introduced method converts the proposed equation by means of collocation points to system of algebraic equations with shifted Chebyshev coefficients. Thus, by solving this system of equations, the shifted Chebyshev coefficients are obtained. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. Numerical results are performed in order to illustrate the usefulness and show the efficiency and the accuracy of the present work.
机译：提出了一种求解四阶积分微分方程的数值方法。此方法基于用一系列已知的平移移位的切比雪夫函数扩展来替换未知函数。介绍了整数导数的近似公式。引入的方法通过搭配点将所提出的方程转换为偏移Chebyshev系数的代数方程组。因此，通过求解该方程组，获得了偏移的切比雪夫系数。特别注意研究收敛性分析并推导所给出的近似公式的误差上限。进行数值结果以说明有用性，并显示本工作的效率和准确性。

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  • 来源
    《Mathematical Problems in Engineering》 |2013年第1期|434753.1-434753.7|共7页
  • 作者

    N. H. Sweilam; M. M. Khader; W. Y. Kota;

  • 作者单位

    Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt;

    Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt;

    Department of Mathematics, Faculty of Science, Mansoura University, Damietta 35516, Egypt;

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