On spectral Petrov-Galerkin method for solving optimal control problem governed by a two-sided fractional diffusion equation

2021/06/19 by Shengyue Li, Li, Shengyue, Wanrong Cao +3
Engineering · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2106.10436

openalex publication_date 2021/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate a spectral Petrov-Galerkin method for an optimal control problem governed by a two-sided space-fractional diffusion-advection-reaction equation. Taking into account the effect of singularities near the boundary generated by the weak singular kernel of the fractional operator, we establish the regularity of the problem in weighted Sobolev space. Error estimates are provided for the presented spectral Petrov-Galerkin method and the convergence orders of the state and control variables are determined. Furthermore, a fast projected gradient algorithm with a quasi-linear complexity is presented to solve the resulting discrete system. Numerical experiments show the validity of theoretical findings and efficiency of the proposed fast algorithm.

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