Error estimate for indirect spectral approximation of optimal control problem governed by fractional diffusion equation with variable diffusivity coefficient

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.07.021 ◽

2021 ◽

Author(s):

Fangyuan Wang ◽

Xiangcheng Zheng ◽

Zhaojie Zhou

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Error Estimate ◽

Control Problem ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Diffusivity Coefficient ◽

Spectral Approximation ◽

Variable Diffusivity

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Time-stepping discontinuous Galerkin approximation of optimal control problem governed by time fractional diffusion equation

Numerical Algorithms ◽

10.1007/s11075-017-0445-3 ◽

2017 ◽

Vol 79 (2) ◽

pp. 437-455 ◽

Author(s):

Zhaojie Zhou ◽

Chenyang Zhang

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Discontinuous Galerkin ◽

Galerkin Approximation ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Stepping ◽

Time Fractional Diffusion Equation

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Legendre pseudo-spectral method for optimal control problem governed by a time-fractional diffusion equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2017.1417591 ◽

2018 ◽

Vol 95 (6-7) ◽

pp. 1308-1325 ◽

Author(s):

Shengyue Li ◽

Zhaojie Zhou

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Spectral Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Fractional Diffusion Equation ◽

Pseudo Spectral Method ◽

Pseudo Spectral

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

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.12.020 ◽

2022 ◽

Vol 107 ◽

pp. 104-116

Author(s):

Shengyue Li ◽

Wanrong Cao ◽

Yibo Wang

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation

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

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.01.018 ◽

2019 ◽

Vol 350 ◽

pp. 331-347

Author(s):

Shengyue Li ◽

Zhaojie Zhou

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Collocation Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Spectral Collocation Method ◽

Spectral Collocation ◽

Space Fractional Diffusion Equation

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A Fast Stochastic Galerkin Method for a Constrained Optimal Control Problem Governed by a Random Fractional Diffusion Equation

Journal of Computational Mathematics ◽

10.4208/jcm.1612-m2016-0696 ◽

2018 ◽

Vol 36 (2) ◽

pp. 259-275

Author(s):

Ning Du and Wanfang Shen

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Galerkin Method ◽

Fractional Diffusion ◽

Constrained Optimal Control ◽

Stochastic Galerkin Method ◽

Stochastic Galerkin ◽

Constrained Optimal Control Problem

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Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.02.019 ◽

2020 ◽

Vol 153 ◽

pp. 234-247 ◽

Author(s):

Xiangcheng Zheng ◽

V.J. Ervin ◽

Hong Wang

Keyword(s):

Diffusion Equation ◽

Error Estimate ◽

Variable Coefficient ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Spectral Approximation

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An Error Estimate of a Numerical Approximation to a Hidden-Memory Variable-Order Space-Time Fractional Diffusion Equation

SIAM Journal on Numerical Analysis ◽

10.1137/20m132420x ◽

2020 ◽

Vol 58 (5) ◽

pp. 2492-2514

Author(s):

Xiangcheng Zheng ◽

Hong Wang

Keyword(s):

Diffusion Equation ◽

Error Estimate ◽

Numerical Approximation ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Variable Order ◽

Time Fractional Diffusion Equation

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A New Optimal $$L^{\infty }(H^1)$$–Error Estimate of a SUSHI Scheme for the Time Fractional Diffusion Equation

Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-030-43651-3_27 ◽

2020 ◽

pp. 305-314

Author(s):

Abdallah Bradji

Keyword(s):

Diffusion Equation ◽

Error Estimate ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Fractional Diffusion Equation

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Optimal control of fractional diffusion equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2010.10.030 ◽

2011 ◽

Vol 61 (1) ◽

pp. 68-78 ◽

Author(s):

Gisèle. M. Mophou

Keyword(s):

Optimal Control ◽

Diffusion Equation ◽

Fractional Diffusion ◽

Fractional Diffusion Equation

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Error estimate on the tanh meshes for the time fractional diffusion equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22656 ◽

2020 ◽

Author(s):

Jiali Zhang ◽

Jizu Huang ◽

Kun Wang ◽

Xin Wang

Keyword(s):

Diffusion Equation ◽

Error Estimate ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Fractional Diffusion Equation

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