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Fractional spectral collocation method for optimal control problem governed by space fractional diffusion equation

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  • Li, Shengyue
  • Zhou, Zhaojie

Abstract

In this paper, we mainly investigate the fractional spectral collocation discretization of optimal control problem governed by a space-fractional diffusion equation. Existence and uniqueness of the solution to optimal control problem is proved. The continuous first order optimality condition is derived. The eigenfunctions of two classes of fractional Strum–Liouville problems are used as basis functions to approximate state variable and adjoint state variable, respectively. The fractional spectral collocation scheme for the control problem is constructed based on ‘first optimize, then discretize’ approach. Note that the solutions of fractional differential equations are usually singular near the boundary, a generalized fractional spectral collocation scheme for the control problem is proposed based on ‘first optimize, then discretize’ approach. A projected gradient algorithm is designed based on the discrete optimality condition. Numerical experiments are carried out to verify the effectiveness of the proposed numerical schemes and algorithm.

Suggested Citation

  • Li, Shengyue & Zhou, Zhaojie, 2019. "Fractional spectral collocation method for optimal control problem governed by space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 331-347.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:331-347
    DOI: 10.1016/j.amc.2019.01.018
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    Cited by:

    1. Taohua Liu & Xiucao Yin & Yinghao Chen & Muzhou Hou, 2023. "A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation," Mathematics, MDPI, vol. 11(8), pages 1-15, April.

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