A posteriori error estimation in maximum norm for a two-point boundary value problem with a Riemann-Liouville fractional derivative

被引：27

作者：

Cen, Zhongdi ^{[1
]}

Liu, Li-Bin ^{[2
]}

Huang, Jian ^{[1
]}

机构：

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

[2] Nanning Normal Univ, Sch Math & Stat, Nanning 530023, Guangxi, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2020年 / 102卷

基金：

美国国家科学基金会;

关键词：

Riemann-Liouville fractional derivative; Boundary value problem; Gronwall inequality; A posteriori error estimate; SYSTEM; MESHES;

D O I：

10.1016/j.aml.2019.106086

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Riemann-Liouville two-point boundary value problem is considered. An integral discretization scheme is developed to approximate the Volterra integral equation transformed from the Rieinann-Liouville boundary value problem. The stability results and a posteriori error analysis are given. A solution-adaptive algorithm based on a posteriori error analysis is designed by equidistributing arc-length monitor function. Numerical experiments are presented to support the theoretical result. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：8

共 9 条

[1] Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems [J].

Das, Pratibhamoy .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 290 :16-25

[2]

Diethlm K., 2010, LECT NOTES MATH, V2004

[3] Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem [J].

Kopteva, N .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2001, 39 (02) :423-441

[4] Maximum norm a posteriori error estimates for a ID singularly perturbed semilinear reaction-diffusion problem [J].

Kopteva, Natalia .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2007, 27 (03) :576-592

[5] Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem [J].

Kopteva, Natalia ;

Stynes, Martin .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2017, 43 (01) :77-99

[6] Finite difference methods with non-uniform meshes for nonlinear fractional differential equations [J].

Li, Changpin ;

Yi, Qian ;

Chen, An .

JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 316 :614-631

[7] ANALYSIS OF A SYSTEM OF SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS WITH STRONG COUPLING [J].

Linss, Torsten .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (03) :1847-1862

[8] A-posteriori error estimation in maximum norm for a strongly coupled system of two singularly perturbed convection-diffusion problems [J].

Liu, Li-Bin ;

Chen, Yanping .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 313 :152-167

[9] A generalized Gronwall inequality and its application to a fractional differential equation [J].

Ye, Haiping ;

Gao, Jianming ;

Ding, Yongsheng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 328 (02) :1075-1081

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