The L~2-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations

Mokhtary P.; Ghoreishi F.

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The L~2-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations

机译：非线性分数阶积分微分方程的Legendre谱Tau矩阵公式的L〜2收敛性

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The operational Tau method, a well known method for solving functional equations is employed to approximate the solution of nonlinear fractional integro-differential equations. The fractional derivatives are described in the Caputo sense. The unique solvability of the linear Tau algebraic system is discussed. In addition, we provide a rigorous convergence analysis for the Legendre Tau method which indicate that the proposed method converges exponentially provided that the data in the given FIDE are smooth. To do so, Sobolev inequality with some properties of Banach algebras are considered. Some numerical results are given to clarify the efficiency of the method.

机译：可操作的Tau方法是一种众所周知的求解函数方程的方法，用于近似非线性分数阶积分微分方程的求解。分数导数在Caputo的意义上进行了描述。讨论了线性Tau代数系统的唯一可解性。此外，我们对Legendre Tau方法进行了严格的收敛性分析，结果表明，只要给定FIDE中的数据是平滑的，该方法就可以呈指数收敛。为此，考虑具有Banach代数某些性质的Sobolev不等式。给出一些数值结果以阐明该方法的效率。

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《Numerical algorithms》 |2011年第4期|共22页
作者
Mokhtary P.; Ghoreishi F.;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Caputo derivative; Fractional integro differential equations; Tau method;

机译：Caputo导数;分数阶积分微分方程;Tau方法;

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1. The L~2-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations [J] . Mokhtary P., Ghoreishi F. Numerical algorithms . 2011,第4期

机译：非线性分数阶积分微分方程的Legendre谱Tau矩阵公式的L〜2收敛性
2. An Efficient Legendre Spectral Tau Matrix Formulation for Solving Fractional Subdiffusion and Reaction Subdiffusion Equations [J] . Doha E. H., Bhrawy A. H., Ezz-Eldien S. S. Journal of Computational and Nonlinear Dynamics . 2015,第2期

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4. Uncertainty Quantification in Fractional Stochastic Integro-Differential Equations Using Legendre Wavelet Collocation Method [C] . Abhishek Kumar Singh, Mani Mehra International Conference on Computational Science . 2020

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5. Multistep linear methods for integro -differential equations of fractional order in Banach spaces [D] . Cuesta Montero, Eduardo. 2001

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7. Generalized Taylor Matrix Method for Solving Multi-Higher Nonlinear Integro-Fractional Differential Equations of Fredholm Type [O] . Bzhween A. Saeed, Main Article Content Shazad Sh. Ahmed 2019

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The L~2-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations

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