Determination of Legendre–Gauss–Lobatto Pseudo–spectral Method for One–Dimensional Advection–Diffusion Equation

Based on Legendre–Gauss–Lobatto zeros and tensor product formulation, we provide a Legendre pseudo–spectral approach for solving one–dimensional parabolic advection–diffusion equations with constant parameters subject to stated beginning and boundary conditions in this chapter. To estimate the unknown function, we first employ differentiation matrices and their derivatives with respect to x and t. Second, we turn our problem into a linear system of equations with unknowns at the collocation locations. Finally, several examples and numerical results are presented to demonstrate the efficacy of the proposed strategy.

Author (S) Details

Galal I. El–Baghdady
Department of Engineering Physics and Mathematics, Faculty of Engineering, Mansoura University, El–Gomheria St., Mansoura, Dakahlia, 35516, Egypt.

M. S. El–Azab
Department of Engineering Physics and Mathematics, Faculty of Engineering, Mansoura University, El–Gomheria St., Mansoura, Dakahlia, 35516, Egypt.

W. S. El–Beshbeshy
Department of Engineering Physics and Mathematics, Faculty of Engineering, Mansoura University, El–Gomheria St., Mansoura, Dakahlia, 35516, Egypt.

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