A Chebyshev spectral collocation method for solving Burgers'-type equations

Authors:
A. H. Khater;R. S. Temsah;M. M. Hassan
Affiliations:
Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;Mathematics Department, Faculty of Science, Minia University, EL-Minia, Egypt
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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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.