Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM
Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM
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DOI：
10.12785/amis/070541
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发表时间：
2013-09-01
影响因子：
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通讯作者：
Mahdy, A. M. S.
中科院分区：
文献类型：
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作者：
Khader, M. M.;Sweilam, N. H.;Mahdy, A. M. S.
本文致力于使用切比雪夫配置方法对由优化问题产生的系统分数微分方程（FDE）进行数值求解。分数阶导数以卡普托意义表示。将所提出的方法应用于 FDE 生成系统会产生可以通过牛顿迭代法求解的代数系统。该方法引入了一种很有前途的工具来求解许多非线性 FDE 系统。提供了两个数值例子来证实所提出方法的准确性和有效性。给出了与分数有限差分法（FDM）和四阶龙格-库塔法（RK4）的比较。
This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated by optimization problem using the Chebyshev collocation method. The fractional derivatives are presented in terms of Caputo sense. The application of the proposed method to the generated system of FDEs leads to algebraic system which can be solved by the Newton iteration method. The method introduces a promising tool for solving many systems of non-linear FDEs. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed methods. Comparisons with the fractional finite difference method (FDM) and the fourth order Runge-Kutta (RK4) are given.