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Legendre–Gauss–Lobatto Pseudo–spectral Method for One–Dimensional Advection–Diffusion Equation |
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PP: 29-35 |
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Author(s) |
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Galal I. El–Baghdady,
M. S. El–Azab,
W. S. El–Beshbeshy,
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Abstract |
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| In this paper, we present a Legendre pseudo–spectral method based on a Legendre–Gauss–Lobatto zeros with the aid of
tensor product formulation for solving one–dimensional parabolic advection–diffusion equation with constant parameters subject to a
given initial condition and boundary conditions. First, we introduce an approximation to the unknown function by using differentiation
matrices and its derivatives with respect to x and t. Secondly , we convert our problem to a linear system of equations to unknowns at the
collocation points, then solve it. Finally, several examples are given and the numerical results are shown to demonstrate the efficiency
of the proposed technique. |
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