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

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 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' equation 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. (c) 2007 Elsevier B.V. All rights reserved.