A Spectral Collocation Method for Solving Caputo-Liouville Fractional Order Fredholm Integro-differential Equations

IF 1 Q1 MATHEMATICS
Khaled Saad, Mustafa Khirallah
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引用次数: 0

Abstract

In this paper, a numerical method for solving the fractional order Fredholm integro-differential equations via the Caputo-Liouville derivative is presented. The method uses the well-known shifted Chebyshev expansion and a truncated series to represent the unknown function. It also incorporates numerical integration techniques like the Trapezoidal, Simpson’s 1/3, and Simpson’s 8/3 methods. The paper also provides an approximation for the derivative of an integer. The procedure converts the provided problem into a system of algebraic equations using shifted Chebyshev coefficients and collocation points. The coefficients are found by solving this system using well-known techniques like Newton’s method. Numerical results are presented graphycally to illustrate the applicability, efficacy, and accuracy of the approach presented in this work. All calculations in this study were performed using the MATHEMATICA software program.
求解卡普托-利乌维尔分数阶弗雷德霍姆积分微分方程的谱配位法
本文提出了一种通过卡普托-利乌维尔导数求解分数阶弗雷德霍姆积分微分方程的数值方法。该方法使用著名的移位切比雪夫展开和截断级数来表示未知函数。它还结合了梯形法、辛普森 1/3 法和辛普森 8/3 法等数值积分技术。论文还提供了整数导数的近似值。该程序利用移位切比雪夫系数和定位点将所提供的问题转换为代数方程系。系数是通过使用牛顿法等著名技术求解该方程组得到的。数值结果以图表形式呈现,以说明本研究中提出的方法的适用性、有效性和准确性。本研究中的所有计算均使用 MATHEMATICA 软件程序进行。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
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