The discontinuous Galerkin finite element approximation of the multi-order fractional initial problems

被引：3

作者：

Zheng, Yunying ^{[1
]}

Zhao, Zhengang ^{[2
]}

Cui, Yanfen ^{[3
]}

机构：

[1] Huaibei Normal Univ, Sch Math Sci, Huaibei 235000, Peoples R China

[2] Shanghai Customs Coll, Dept Fundamental Courses, Shanghai 201204, Peoples R China

[3] Shanghai Univ, Sch Sci, Dept Math, Shanghai 200444, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 348卷

基金：

中国国家自然科学基金;

关键词：

Multi-order fractional differential equation; Caputo derivative; Galerkin finite element method; Discontinuous Galerkin finite element method; Stability; LANGEVIN EQUATION; ERROR ANALYSIS; FORMULATION;

D O I：

10.1016/j.amc.2018.11.057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct a discontinuous Galerkin finite element scheme for the multi-order fractional ordinary differential equation. The analysis of the stability shows the scheme is L-2 stable. The existence and uniqueness of the numerical solution are discussed in detail. The convergence study gives the approximation orders under L-2 norm and L-infinity norm. Numerical examples demonstrate the effectiveness of the theoretical results. The oscillation phenomena are also found during numerical tracing a non-linear multi-order fractional initial problem. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：257 / 269

页数：13

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