A posteriori error analysis for a fractional differential equation

被引：15

作者：

Cen, Zhongdi ^{[1
]}

Le, Anbo ^{[1
]}

Xu, Aimin ^{[1
]}

机构：

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

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2017年 / 94卷 / 06期

关键词：

Fractional differential equation; Caputo fractional derivative; finite difference scheme; a posteriori error estimate; mesh equidistribution; 65L05; 65L12; 65L20; REACTION-DIFFUSION PROBLEM; BOUNDARY-VALUE-PROBLEMS; UNIFORM-CONVERGENCE ANALYSIS; SPLINE COLLOCATION; APPROXIMATIONS; CONVECTION;

D O I：

10.1080/00207160.2016.1184263

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Numerical treatment for a fractional differential equation (FDE) is proposed and analysed. The solution of the FDE may be singular near certain domain boundaries, which leads to numerical difficulty. We apply the upwind finite difference method to the FDE. The stability properties and a posteriori error analysis for the discrete scheme are given. Then, a posteriori adapted mesh based on a posteriori error analysis is established by equidistributing arc-length monitor function. Numerical experiments illustrate that the upwind finite difference method on a posteriori adapted mesh is more accurate than the method on uniform mesh.

引用

页码：1185 / 1195

页数：11

共 35 条

[1]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[2]

[Anonymous], 2006, Journal of the Electrochemical Society

[3]

Baffet D., J SCI COMPUT, DOI [10.1007/s10915-015-0089-1, DOI 10.1007/S10915-015-0089-1.]

[4]

Cao G. -H., 2015, J COMPUT PHYS, V280, P510, DOI [10.1016/j.jcp.2014.09.033, DOI 10.1016/J.JCP.2014.09.033]

[5] Uniform convergence analysis of finite difference approximations for singular perturbation problems on an adapted grid [J].

Chen, YP .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2006, 24 (1-4) :197-212

[6] 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

[7]

Diethlm K., 2010, LECT NOTES MATH, V2004

[8] Application of the collocation method for solving nonlinear fractional integro-differential equations [J].

Eslahchi, M. R. ;

Dehghan, Mehdi ;

Parvizi, M. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 257 :105-128

[9] Least squares finite-element solution of a fractional order two-point boundary value problem [J].

Fix, GJ ;

Roop, JP .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2004, 48 (7-8) :1017-1033

[10] Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems [J].

Gracia, J. L. ;

Stynes, M. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 273 :103-115

← 1 2 3 4 →