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Chebyshev–Gauss–Lobatto Pseudo–spectral Method for One–Dimensional Advection–Diffusion Equation with Variable coefficients |
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PP: 7-14 |
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doi:10.18576/sjm/030102
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Author(s) |
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Galal I. El–Baghdady,
M. S. El–Azab,
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Abstract |
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| In this paper, we present a Chebyshev pseudo–spectral method based on a Chebyshev–Gauss–Lobatto zeros with the aid
of the Kronecker product formulation for solving one–dimensional parabolic advection–diffusion equation with variable coefficients
subject to a given initial condition and boundary conditions. First, we introduce an approximation to the unknown function by using
Chebyshev differentiation matrices and its derivatives with respect to space x and time t. Secondly , we convert our problem to a linear
system of equations to unknowns at the collocation points, then solve it. Finally, two examples are given to illustrate the validity and
applicability of the proposed technique with the aid of L¥-norm error and L2-norm error to the exact solution. A comparison between
the presented method has been done with cubic B-Spline finite difference method. |
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