A space-time spectral method for the time fractional diffusion optimal control problems

Advances in Difference Equations

Chuanju Xu¹  Xingyang Ye² 

[1] School of Mathematical Sciences, Xiamen University, Xiamen, China;School of Science, Jimei University, Xiamen, China

关键词: fractional optimal control problem;    time fractional diffusion equation;    spectral method;    a priori error;   

DOI  :  10.1186/s13662-015-0489-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the Galerkin spectral approximation to an unconstrained convex distributed optimal control problem governed by the time fractional diffusion equation. We construct a suitable weak formulation, study its well-posedness, and design a Galerkin spectral method for its numerical solution. The contribution of the paper is twofold: a priori error estimate for the spectral approximation is derived; a conjugate gradient optimization algorithm is designed to efficiently solve the discrete optimization problem. In addition, some numerical experiments are carried out to confirm the efficiency of the proposed method. The obtained numerical results show that the convergence is exponential for smooth exact solutions.

【 授权许可】

CC BY