Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separa...

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Main Authors: Jiaqi Zhong, Cheng Zeng, Yupeng Yuan, Yuzhe Zhang, Ye Zhang
Format: Article
Language:English
Published: AIP Publishing LLC 2018-04-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/1.5023332
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spelling doaj-952fac4087ce4046a23b86345b70f0752020-11-25T00:18:45ZengAIP Publishing LLCAIP Advances2158-32262018-04-0184045314045314-1110.1063/1.5023332061804ADVNumerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin methodJiaqi Zhong0Cheng Zeng1Yupeng Yuan2Yuzhe Zhang3Ye Zhang4College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaCollege of Science, Guizhou Institute of Technology, Guiyang 550003, ChinaChongqing Acoustic-Optic-Electronic Co., Ltd, China Electronics Technology Group Corporation, Chongqing 401332, ChinaChongqing Acoustic-Optic-Electronic Co., Ltd, China Electronics Technology Group Corporation, Chongqing 401332, ChinaSchool of Software Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThe aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.http://dx.doi.org/10.1063/1.5023332
collection DOAJ
language English
format Article
sources DOAJ
author Jiaqi Zhong
Cheng Zeng
Yupeng Yuan
Yuzhe Zhang
Ye Zhang
spellingShingle Jiaqi Zhong
Cheng Zeng
Yupeng Yuan
Yuzhe Zhang
Ye Zhang
Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method
AIP Advances
author_facet Jiaqi Zhong
Cheng Zeng
Yupeng Yuan
Yuzhe Zhang
Ye Zhang
author_sort Jiaqi Zhong
title Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method
title_short Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method
title_full Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method
title_fullStr Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method
title_full_unstemmed Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method
title_sort numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral galerkin method
publisher AIP Publishing LLC
series AIP Advances
issn 2158-3226
publishDate 2018-04-01
description The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.
url http://dx.doi.org/10.1063/1.5023332
work_keys_str_mv AT jiaqizhong numericalsolutionoftheunsteadydiffusionconvectionreactionequationbasedonimprovedspectralgalerkinmethod
AT chengzeng numericalsolutionoftheunsteadydiffusionconvectionreactionequationbasedonimprovedspectralgalerkinmethod
AT yupengyuan numericalsolutionoftheunsteadydiffusionconvectionreactionequationbasedonimprovedspectralgalerkinmethod
AT yuzhezhang numericalsolutionoftheunsteadydiffusionconvectionreactionequationbasedonimprovedspectralgalerkinmethod
AT yezhang numericalsolutionoftheunsteadydiffusionconvectionreactionequationbasedonimprovedspectralgalerkinmethod
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