An efficient numerical method for a Riemann-Liouville two-point boundary value problem

被引：4

作者：

Huang, Jian ^{[1
]}

Cen, Zhongdi ^{[1
]}

Liu, Li-Bin ^{[2
]}

Zhao, Jialiang ^{[1
]}

机构：

[1] Zhejiang Wanli Univ, Inst Math, Ningbo 315100, Peoples R China

[2] Nanning Normal Univ, Sch Math & Stat, Nanning 530299, Guangxi, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2020年 / 103卷

基金：

美国国家科学基金会;

关键词：

Fractional differential equation; Riemann-Liouville fractional derivative; Volterra integral equation; Gronwall inequality; Mesh equidistribution; APPROXIMATIONS; MESHES;

D O I：

10.1016/j.aml.2019.106201

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper a numerical method is considered for a two-point boundary value problem with a Riemann-Liouville fractional derivative, where the exact solution may have weak singularity. The linear interpolation is used to approximate the functions in the fractional integral transformed from the Riemann-Liouville boundary value problem. In order to capture the singular phenomena of the exact solution, an adaptive mesh is developed by equidistributing a monitor function. The stability is derived by a modified Gronwall inequality. It is shown that the scheme is second-order convergent. Numerical experiments are provided to demonstrate the theoretical results. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：8

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