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A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations

机译:Chebyshev多项式分数积分的新公式:在求解多项式分数阶微分方程中的应用

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摘要

A new explicit formula for the integrals of shifted Chebyshev polynomials of any degree for any fractional-order in terms of shifted Chebyshev polynomials themselves is derived. A fast and accurate algorithm is developed for the solution of linear multi-order fractional differential equations (FDEs) by considering their integrated forms. The shifted Chebyshev spectral tau (SCT) method based on the integrals of shifted Chebyshev polynomials is applied to construct the numerical solution for such problems. The method is then tested on examples. It is shown that the SCT yields better results.
机译:对于移位切比雪夫多项式本身,针对任何分数阶的任何程度的移位切比雪夫多项式的积分,得出了一个新的显式公式。通过考虑线性多阶分数阶微分方程的积分形式,开发了一种快速准确的算法。应用基于偏移切比雪夫多项式积分的偏移切比雪夫谱τ(SCT)方法构造此类问题的数值解。然后在示例中测试该方法。结果表明,SCT产生更好的结果。

著录项

  • 来源
    《Applied Mathematical Modelling》 |2013年第6期|4245-4252|共8页
  • 作者单位

    Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia,Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;

    Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia,Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;

    Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA;

  • 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

    Multi-term FDEs; Tau method; Shifted Chebyshev polynomials; Chebyshev-Gauss quadrature; Riemann-Liouville sense;

    机译:长期FDE;牛头法;移位的切比雪夫多项式;Chebyshev-Gauss正交;黎曼-利维尔感;

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