Fejér-Quadrature Collocation Algorithm for Solving Fractional Integro-Differential Equations via Fibonacci Polynomials

Y. H. Youssri, A. G. Atta
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Abstract

In this article, we introduce a novel spectral algorithm utilizing Fibonacci polynomials to numerically solve both linear and nonlinear integro-differential equations with fractional-order derivatives. Our approach employs a quadrature-collocation method, transforming complex equations and associated conditions into systems of linear or nonlinear algebraic equations. The solutions to these equations, involving unknown coefficients, provide accurate numerical approximations for the original fractional-order equations. To validate the method, we present numerical examples illustrating its robustness and versatility. Comparative analyses with available analytical solutions affirm the reliability and accuracy of our algorithm, establishing its practical utility in addressing fractional-order integro-differential equations. This research contributes to computational mathematics and spectral methods, offering a promising tool for diverse scientific and engineering challenges.
通过 Fibonacci 多项式求解分数积分微分方程的 Fejér-Quadrature 协整算法
在本文中,我们介绍了一种利用斐波那契多项式的新型谱算法,用于数值求解具有分数阶导数的线性和非线性积分微分方程。我们的方法采用正交定位法,将复杂方程和相关条件转化为线性或非线性代数方程系统。这些方程的解涉及未知系数,为原始分数阶方程提供了精确的数值近似值。为了验证该方法,我们提供了数值示例,说明其稳健性和多功能性。与现有分析解的比较分析肯定了我们算法的可靠性和准确性,确立了它在处理分数阶积分微分方程中的实用性。这项研究为计算数学和光谱方法做出了贡献,为应对各种科学和工程挑战提供了一种前景广阔的工具。
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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