Title : ( A numerical method based on a bilinear pseudo-spectral method to solve the convection-diffusion optimal control problems )
Authors: Fereshteh Samadi , Aghileh Heydari , Sohrab Effati ,
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Abstract
In this paper, we consider the bilinear pseudo-spectral method for solving convectiondiffusion optimal control problems (OCPs). First, we convert the optimal control problem to a partial differential equation (PDE) system including the state equation of the original problem and the adjoint equation which must be solved. Next, we approximate the coupled system by a bilinear pseudo-spectral method based on Chebyshev polynomials and obtain a coupled Sylvester system and then use some iterative and direct methods to solve it. We used bilinear pseudo-spectral method to have simplicity in implementation and Chebyshev polynomials to have accuracy and stability. Robustness and accuracy of the method are verified by solving some numerical experiments.
Keywords
, Convection-diffusion equation, Optimal control, Bilinear pseudo-spectral method, Coupled Sylvester system, Chebyshev polynomials
@article{paperid:1079448,
author = {فرشته صمدی and عقیله حیدری and Effati, Sohrab},
title = {A numerical method based on a bilinear pseudo-spectral method to solve the convection-diffusion optimal control problems},
journal = {International Journal of Computer Mathematics},
year = {2020},
volume = {98},
number = {1},
month = {February},
issn = {0020-7160},
pages = {28--46},
numpages = {18},
keywords = {Convection-diffusion equation; Optimal control; Bilinear pseudo-spectral method;
Coupled Sylvester system; Chebyshev polynomials},
}
%0 Journal Article
%T A numerical method based on a bilinear pseudo-spectral method to solve the convection-diffusion optimal control problems
%A فرشته صمدی
%A عقیله حیدری
%A Effati, Sohrab
%J International Journal of Computer Mathematics
%@ 0020-7160
%D 2020
