Numerical solution of linear fractional weakly singular integro-differential equations with integral boundary conditions

Arvet Pedas; Enn Tamme; Mikk Vikerpuur

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Numerical solution of linear fractional weakly singular integro-differential equations with integral boundary conditions

机译：具有积分边界条件的线性分数阶弱奇异积分微分方程的数值解

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摘要

We consider a class of boundary value problems for linear fractional weakly singular integro-differential equations with Caputo fractional derivatives and integral boundary conditions. Using an integral equation reformulation of the boundary value problem, we first study the regularity of the exact solution and its Caputo derivative. Based on the obtained regularity properties and by using suitable smoothing transformations along with spline collocation techniques, the numerical solution of the problem is discussed. Optimal global convergence estimates are derived and a superconvergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented.

机译：我们考虑带有Caputo分数阶导数和积分边界条件的线性分数阶弱奇异积分-微分方程的一类边值问题。我们使用边界值问题的积分方程式重构，首先研究精确解及其Caputo导数的正则性。基于获得的规则性，并通过使用合适的平滑变换以及样条搭配技术，讨论了该问题的数值解。得出了最佳的全局收敛估计，并给出了针对网格和配置参数的特殊选择的超收敛结果。还提供了一个数字说明。

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来源
《Applied numerical mathematics》 |2020年第3期|124-140|共17页
作者
Arvet Pedas; Enn Tamme; Mikk Vikerpuur;
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作者单位

Institute of Mathematics and Statistics University of Tartu liivi 2 50409 Tartu Estonia;

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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
Fractional weakly singular; integro-differential equation; Caputo derivative; Boundary value problem; Smoothing transformation; Spline collocation method; Graded grid;

机译：分数弱奇异;积分微分方程Caputo衍生物;边值问题;平滑转换;样条搭配方法;渐变网格;

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1. On the numerical solution of a class of linear fractional integro-differential algebraic equations with weakly singular kernels [J] . Ghanbari F., Mokhtary P., Ghanbari K. Applied numerical mathematics . 2019,第OCTa期

机译：一类具有弱奇异核的线性分数阶积分-微分代数方程的数值解
2. On the numerical solution of a class of linear fractional integro-differential algebraic equations with weakly singular kernels [J] . Ghanbari F., Mokhtary P., Ghanbari K. Applied numerical mathematics . 2019,第Octa期

机译：用弱奇异核的一类线性分数叠加代数等级的数值解
3. Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions [J] . Nemati S., Lima P. M. Applied mathematics and computation . 2018,第期

机译：帽函数修改的弱奇异内核非线性分数积分微分方程的数值解
4. Numerical solution of fractional integro-differential equations with weakly singular kernels [C] . Arvet Pedas, Enn Tamme, Mikk Vikerpuur International Conference of Numerical Analysis and Applied Mathematics . 2019

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5. CONVERGENCE AND SUPERCONVERGENCE OF NUMERICAL SOLUTIONS OF WEAKLY SINGULAR INTEGRAL AND DIFFERENTIAL EQUATIONS (GALERKIN, COLLOCATION, EIGENVALUES, EIGENVECTORS, SPLINES) [D] . LEBBAR, RACHID. 1986

机译：弱奇异积分和微分方程数值解的收敛性和超级度验收（Galerkin，Collocation，特征值，特征向量，花键）
6. A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things [O] . Rohul Amin, Shah Nazir, Iván García-Magariño 2020

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7. Weak solutions for some nonlinear fractional differential equations with fractional integral boundary conditions in Banach spaces [O] . 2019

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8. Numerical Quadrature Methods for Integrals of Singular Periodic Functions and Their Application to Singular and Weakly Singular Integral Equations [R] . Sidi, A., Israeli, M. 1986

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Numerical solution of linear fractional weakly singular integro-differential equations with integral boundary conditions

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