High order approximations of solutions to initial value problems for linear fractional integro-differential equations

被引：5

作者：

Ford, Neville J. ^{[1
]}

Pedas, Arvet ^{[2
]}

Vikerpuur, Mikk ^{[2
]}

机构：

[1] Univ Chester, Parkgate Rd, Chester CH1 4BJ, England

[2] Univ Tartu, Inst Math & Stat, Narva St 18, Tartu, Estonia

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2023年 / 26卷 / 05期

关键词：

fractional differential equation; Weakly singular kernel; Caputo derivative; Initial value problem; Smoothing transformation; Collocation method; PIECEWISE POLYNOMIAL COLLOCATION; VOLTERRA INTEGRAL-EQUATIONS; SPLINE COLLOCATION; NUMERICAL-SOLUTION; SMOOTHING TRANSFORMATION; DIFFERENTIAL-EQUATIONS; DERIVATIVES; CALCULUS; KERNELS;

D O I：

10.1007/s13540-023-00186-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a general class of linear integro-differential equations with Caputo fractional derivatives and weakly singular kernels. First, the underlying initial value problem is reformulated as an integral equation and the possible singular behavior of its exact solution is determined. After that, using a suitable smoothing transformation and spline collocation techniques, the numerical solution of the problem is discussed. Optimal convergence estimates are derived and a superconvergence result of the proposed method is established. The obtained theoretical results are supported by numerical experiments.

引用

页码：2069 / 2100

页数：32

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