A Chebyshev spectral collocation method for solving Burgers'-type equations
By A. H. Khater, R. S. Temsah, M. M. Hassan. 2008
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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.
Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/97dec1a7237ac50fb33e24ea28e5087a8aa932de
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Citations in the corpus
- A differential quadrature method for numerical solutions of Burgers'‐type equations (2012, methodology): “Comparison of numerical values of u for the Example 4 with those obtained by Khater et al. (2008) and Rashid (2009) with a0 1⁄4 0.”