Spline collocation for fractional weakly singular integro-differential equations

被引：26

作者：

Pedas, Arvet ^{[1
]}

Tamme, Enn ^{[1
]}

Vikerpuur, Mikk ^{[1
]}

机构：

[1] Univ Tartu, Inst Math & Stat, Liivi 2, EE-50409 Tartu, Estonia

来源：

APPLIED NUMERICAL MATHEMATICS | 2016年 / 110卷

关键词：

Fractional weakly singular integro-differential equation; Caputo derivative; Boundary value problem; Collocation method; Graded grid; BOUNDARY-VALUE-PROBLEMS; PIECEWISE POLYNOMIAL COLLOCATION; ORDER NUMERICAL-METHODS; DIFFERENTIAL-EQUATIONS; CALCULUS; KERNELS;

D O I：

10.1016/j.apnum.2016.07.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of boundary value problems for linear fractional weakly singular integro-differential equations which involve Caputo-type derivatives. Using an integral equation reformulation of the boundary value problem, we first study the regularity of the exact solution. Based on the obtained regularity properties and spline collocation techniques, the numerical solution of the boundary value problem by suitable non polynomial approximations is discussed. Optimal global convergence estimates are derived and a super-convergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented. (C) 2016 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：204 / 214

页数：11

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