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

被引：15

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 | 2020年 / 149卷

关键词：

Fractional weakly singular integro-differential equation; Caputo derivative; Boundary value problem; Smoothing transformation; Spline collocation method; Graded grid; PIECEWISE POLYNOMIAL COLLOCATION; SPLINE COLLOCATION; SMOOTHING TRANSFORMATION; DIFFERENTIAL-EQUATIONS; ERROR ANALYSIS;

D O I：

10.1016/j.apnum.2019.07.014

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 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. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：124 / 140

页数：17

共 36 条

[1] Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels [J].