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.
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页数：8
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