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A Chebyshev-Gauss-Radau Scheme For Nonlinear Hyperbolic System Of First Order |
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PP: 535-544 |
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Author(s) |
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E. H. Doha,
A. H. Bhrawy,
R. M. Hafez,
M. A. Abdelkawy,
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Abstract |
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| A numerical approximation of the initial-boundary system of nonlinear hyperbolic equations based on spectral collocation
method is presented in this article. A Chebyshev-Gauss-Radau collocation (C-GR-C) method in combination with the implicit Runge-
Kutta scheme are employed to obtain highly accurate approximations to the mentioned problem. The collocation points are the
Chebyshev interpolation nodes. This approach reduces this problem to solve system of nonlinear ordinary differential equations which
are far easier to be solved. Indeed, by selecting a limited number of collocation nodes, we obtain an accurate results. The numerical
examples demonstrate the accuracy, efficiency, and versatility of the method. |
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