A Chebyshev spectral collocation method for solving Burgers’-type equations |
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Authors: | AH Khater RS Temsah MM Hassan |
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Institution: | 1. Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;2. Mathematics Department, Faculty of Science, Minia University, EL-Minia, Egypt |
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Abstract: | In this paper, we elaborated a spectral collocation method based on differentiated Chebyshev polynomials to obtain numerical solutions for some different kinds of nonlinear partial differential equations. The problem is reduced to a system of ordinary differential equations that are solved by Runge–Kutta method of order four. Numerical results for the nonlinear evolution equations such as 1D Burgers’, KdV–Burgers’, coupled Burgers’, 2D Burgers’ and system of 2D Burgers’ equations are obtained. The numerical results are found to be in good agreement with the exact solutions. Numerical computations for a wide range of values of Reynolds’ number, show that the present method offers better accuracy in comparison with other previous methods. Moreover the method can be applied to a wide class of nonlinear partial differential equations. |
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Keywords: | 35Q53 74G15 74J30 74J35 74J40 74S25 |
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