A New Solution for Optimal Control of Fractional Convection–Reaction–Diffusion Equation Using Rational Barycentric Interpolation

被引：1
作者：
Majid Darehmiraki
Arezou Rezazadeh
机构：
[1] Behbahan Khatam Alanbia University of Technology,Department of Mathematics
[2] University of Qom,Department of Mathematics
来源：
Bulletin of the Iranian Mathematical Society | 2020年 / 46卷
关键词：
Optimal control; Partial differential equation; Convection–reaction fractional equation; Grünwald–Letnikov formula; Barycentric collocation method; 43A62; 42C15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper solves an optimal control problem governed by a fractional convection–reaction–diffusion partial differential equation. Using Lagrangian multipliers, necessary conditions are obtained, and then, Barycentric collocation method are applied for discretizing classical derivatives and Grünwald–Letnikov formula for fractional derivative. Barycentric interpolation is a class of Lagrange polynomial interpolation that is fast and deserves to be known as a method of polynomial interpolation and Grünwald–Letnikov formula is a basic extension of the derivative in fractional calculus. Numerical examples are presented to show the effectiveness of the method.
引用
收藏
页码：1307 / 1340
页数：33
相关论文
共 65 条
[1]  
Acosta G(2017)A fractional Laplace equation: regularity of solutions and finite element approximations SIAM J. Numer. Anal. 55 472-495
[2]  
Borthagaray JP(2015)A FEM for an optimal control problem of fractional powers of elliptic operators SIAM J. Control Optim. 53 3432-3456
[3]  
Antil H(2016)A space-time fractional optimal control problem: analysis and discretization SIAM J. Control Optim. 54 1295-1328
[4]  
Otarola E(2004)Barycentric lagrange interpolation SIAM Rev. 46 501-517
[5]  
Antil H(2002)Practical methods for optimal control using nonlinear programming Appl. Mech. Rev. 55 B68-47
[6]  
Otárola E(2016)A new spectral algorithm for a time-space fractional partial differential equations with subdiffusion and superdiffusion Proc. Rom. Acad. Ser. A 17 39-180
[7]  
Salgado AJ(2016)A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation Numer. Algorithms 71 151-2110
[8]  
Berrut JP(2015)Numerical approximation of fractional powers of elliptic operators Math. Comput. 84 2083-395
[9]  
Trefethen LN(2009)Multigrid methods for PDE optimization SIAM Rev. 51 361-2164
[10]  
Betts JT(2016)A novel method to solve a class of distributed optimal control problems using Bezier curves J. Comput. Nonlinear Dyn. 11 061008-331
1234567