A posteriori error estimates of spectral method for the fractional optimal control problems with non-homogeneous initial conditions

被引：4

作者：

Ye, Xingyang ^{[1
]}

Xu, Chuanju ^{[2
,3
]}

机构：

[1] Jimei Univ, Sch Sci, Xiamen 361021, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[3] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Peoples R China

来源：

AIMS MATHEMATICS | 2021年 / 6卷 / 11期

关键词：

fractional optimal control problem; initial conditions; spectral method; a posteriori error; DIFFUSION EQUATION; APPROXIMATION;

D O I：

10.3934/math.2021697

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider an optimal control problem governed by a space-time fractional diffusion equation with non-homogeneous initial conditions. A spectral method is proposed to discretize the problem in both time and space directions. The contribution of the paper is threefold: (1) A discussion and better understanding of the initial conditions for fractional differential equations with Riemann-Liouville and Caputo derivatives are presented. (2) A posteriori error estimates are obtained for both the state and the control approximations. (3) Numerical experiments are performed to verify that the obtained a posteriori error estimates are reliable.

引用

页码：12028 / 12050

页数：23

共 33 条

[21] Otarola E, 2020, ARXIV200713848
[22] An adaptive finite element method for the sparse optimal control of fractional diffusion
Otarola, Enrique
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 36 (02) : 302 - 328
[23] Podlubny I., 1999, FRACTIONAL DIFFERENT
[24] QUARTERONI A., 2008, Springer Ser. Comput. Math., V23
[25] A spectral Galerkin approximation of optimal control problem governed by fractional advection-diffusion-reaction equations
Wang, Fangyuan
Zhang, Zhongqiang
Zhou, Zhaojie
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 386
[26] A fast second-order parareal solver for fractional optimal control problems
Wu, Shu-Lin
Huang, Ting-Zhu
[J]. JOURNAL OF VIBRATION AND CONTROL, 2018, 24 (15) : 3418 - 3433
[27] Ye X., 2014, SPECTRAL HIGH ORDER, P403
[28] [叶星旸 Ye Xingyang], 2016, [中国科学. 数学, Scientia Sinica Mathematica], V46, P1053
[29] A space-time spectral method for the time fractional diffusion optimal control problems
Ye, Xingyang
Xu, Chuanju
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2015,
[30] A posteriori error estimates for the fractional optimal control problems
Ye, Xingyang
Xu, Chuanju
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015, : 1 - 13

← 1 2 3 4 →