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

Darehmiraki, Majid; Rezazadeh, Arezou

doi:10.1007/s41980-019-00327-y

Cited by 6 publications

(1 citation statement)

References 34 publications

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“…All the method mentioned so far, belong to discretize‐then‐optimize algorithms. On the other hand, for the optimize‐then‐discretize the constraints should be transformed to an algebraic system by using different methods such as FEM, finite difference method, or other existing method for discretization [6, 7, 21].…”

Section: Introductionmentioning

confidence: 99%

An interpolation method for the optimal control problem governed by the elliptic convection–diffusion equation

Darehmiraki

Rezazadeh

Ahmadian

et al. 2020

Numerical Methods Partial

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We know that due to the Weierstrass approximation theorem any continuous function over a closed interval can be approximated by a polynomial of sufficiently high degree. Therefore, they are frequently used to approximate functions. We proposed a Lagrange polynomial‐based approach for solving the optimal control problem governed by the elliptic convection–diffusion partial differential equation. This paper solves it by the barycentric interpolation method as a class of strong‐form numerical methods. Thanks to Lagrangian multipliers, optimality system is derived and then the barycentric collocation method is employed to discretize the state variable and adjoint variable. Barycentric interpolation method is a Lagrange polynomial interpolation that is fast and deserves to be known as a method of polynomial interpolation. The convergence of the proposed method is also proved. At the end, numerical experiments are employed to illustrate the theoretical findings.

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Section: Introductionmentioning

confidence: 99%