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Space–Time Spectral Collocation Method for Solving Burgers Equations with the Convergence Analysis

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College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
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Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 3619995161, Iran
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Department of Applied Mathematics, Sorbonne University, 75005 Paris, France
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Department of Mathematics, Kosar University of Bojnord, Bojnord P. O. Box 9415615458, Iran
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Department of Mathematics and Applied Mathematics, University of Venda, P. Bag X5050, Thohoyandu 0950, South Africa
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Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1439; https://doi.org/10.3390/sym11121439
Received: 27 August 2019 / Revised: 3 October 2019 / Accepted: 4 October 2019 / Published: 22 November 2019
This article deals with a numerical approach based on the symmetric space-time Chebyshev spectral collocation method for solving different types of Burgers equations with Dirichlet boundary conditions. In this method, the variables of the equation are first approximated by interpolating polynomials and then discretized at the Chebyshev–Gauss–Lobatto points. Thus, we get a system of algebraic equations whose solution is the set of unknown coefficients of the approximate solution of the main problem. We investigate the convergence of the suggested numerical scheme and compare the proposed method with several recent approaches through examining some test problems. View Full-Text
Keywords: Burgers equation; Chebyshev spectral collocation method; Chebyshev–Gauss–Lobatto nodes; convergence analysis Burgers equation; Chebyshev spectral collocation method; Chebyshev–Gauss–Lobatto nodes; convergence analysis
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Huang, Y.; Skandari, M.H.N.; Mohammadizadeh, F.; Tehrani, H.A.; Georgiev, S.G.; Tohidi, E.; Shateyi, S. Space–Time Spectral Collocation Method for Solving Burgers Equations with the Convergence Analysis. Symmetry 2019, 11, 1439.

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